Golden balls: A prisoner's dilemma experiment

Darai, Donja; Grätz, Silvia

Working Paper

Working Paper, No. 1006

Provided in Cooperation with:

Socioeconomic Institute (SOI), University of Zurich

Suggested Citation: Darai, Donja; Grätz, Silvia (2010) : Golden balls: A prisoner's dilemma experiment,

Working Paper, No. 1006, University of Zurich, Socioeconomic Institute, Zurich

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Socioeconomic Institute

Sozialökonomisches Institut

Working Paper No. 1006

Golden Balls: A Prisoner’s Dilemma Experiment

Donja Darai, Silvia Grätz

July 2010

Socioeconomic Institute

University of Zurich

Working Paper No. 1006

Golden Balls: A Prisoner’s Dilemma Experiment

July 2010

Author's address: Donja Darai

E-mail: [email protected]

Silvia Grätz

E-mail: [email protected]

Publisher Sozialökonomisches Institut

Bibliothek (Working Paper)

Rämistrasse 71

CH-8006 Zürich

Phone: +41-44-634 21 37

Fax: +41-44-634 49 82

URL: www.soi.uzh.ch

E-mail: [email protected]

Golden Balls: A Prisoner’s Dilemma Experiment

∗

Donja Darai and Silvia Gr

atz

†

This Version: July 2010

Abstract

We analyze cooperative behavior in a prisoner’s dilemma game with high stakes, face-to-face

communication, and two rounds of pre-play in which the two ﬁnal contestants are endoge-

nously selected via a voting process. Using data from the British television game show

“Golden Balls”, we ﬁnd a unilateral cooperation rate of 55% and a mutual cooperation rate

of 33%. The stake size is on average £13,300 and ranges from £3 to £100,150. Our analy-

sis shows that both stake size and communication have a signiﬁcant impact on the player’s

likelihood to cooperate. In particular, we observe a negative correlation between stake size

and cooperation. Also certain gestures, as handshakes, decrease the likelihood to cooper-

ate. But, if players mutually promise each other to cooperate and in addition shake hands

on it, the cooperation rate increases. We also show that a player’s expectation about the

stake size matters. Further, we ﬁnd a strong link between contestant’s pre-play behavior and

the outcome of the prisoner’s dilemma. Players who contribute more to the stake size are

less likely to cooperate, even though each player’s contribution is determined by a random

process. Apart from that, it matters whether a player has lied in the pre-play and whether

she experienced her opponent’s goodwill. Addressing the partner selection process, we ﬁnd

that contestant’s voting decisions are based on objective criteria, i.e., their opponent’s mon-

etary contribution to the stake size, as well as subjective personal characteristics, i.e., the

opponents’ trustworthiness.

∗

The authors thank Armin Schmutzler, Nick Netzer, Kevin Staub, the seminar participants in Zurich, and the

participants of the ESA Meeting 2010 in Copenhagen for helpful comments and suggestions as well as Max Pﬁster

for excellent research assistance. Financial support of the Swiss National Foundation is gratefully acknowledged.

The data were provided to the authors by the television show producers, courtesy of Endemol UK plc.

†

Both authors: Department of Economics, University of Zurich, Bl

umlisalpstrasse 10, CH-8006 Zurich.

1 Introduction

The well known prisoner’s dilemma game has become the classic economic example to demon-

strate non-cooperative behavior: Two contestants face a “dilemma” in which, independent of

the other’s action, each player is better oﬀ by defection than by cooperation. But, the outcome

obtained when both defect is worse for each player than the outcome they would have obtained

if both had cooperated. Thus, self-interested behavior does not unequivocally lead to a globally

optimal solution. A common view is that this puzzle illustrates a conﬂict between individual

and group rationality. Two players who both pursue rational self-interest may all end up worse

oﬀ than if both act contrary to rational self-interest.

In contrast to the majority of experiments carried out, this paper analyzes cooperative behavior

in an environment of high stakes and face-to-face communication between players. Players are

not only allowed to talk to each other, but they have the possibility to play with each other, and

thereby get to know each other in two stages of pre-play. For our analysis we use data from the

British television game show “Golden Balls”. The show consists of three rounds, the ﬁrst two

are pre-play and in the third two contestants play a prisoner’s dilemma with defection being a

weakly dominant strategy. Starting with four contestants, each round every player is randomly

assigned a certain cash value. The values are partly common knowledge and partly private infor-

mation for the respective player. The players then make truthful or untruthful statements about

their values. At the end of each round, each player has to cast a vote against one of the other

players. The one who receives the majority of votes has to leave the show empty-handed and her

values are taken out of the game. Therefore the selection determines the two ﬁnal players and

the stake size at the same time. The two ﬁnal players decide about the division of the stakes via

playing a prisoner’s dilemma. Before the dilemma is played, both players are allowed to discuss

with each other.

Our contribution consists not only of (i) the analysis of cooperative behavior in the presence

of high stakes and communication, but also of (ii) the analysis of the players’ behavior in the

pre-play, especially their voting decisions with respect to its inﬂuence on the outcome of the

prisoner’s dilemma.

Concerning cooperative behavior, we observe a unilateral cooperation rate of 55% and a mutual

cooperation rate of 33%. We ﬁnd that both stake size and communication have a signiﬁcant

impact on the cooperation rate. Our analysis shows a negative correlation between the stake

size and the cooperation rate with a substantial decline around the level of £500. In games

with stakes below that value, the unilateral cooperation rate even increases to 74%, and the mu-

tual cooperation rate to 56%. Further, we can show that player’s expectation about the stake

size matters. If the jackpot is lower than expected, the players are more likely to cooperate.

With respect to communication, certain words and gestures are more important than others.

Mutually promising each other to cooperate and shaking hands on it increases the cooperation

rate, whereas shaking hands without a promise leads to a decline. Apart from those eﬀects,

demographic characteristics, such as age and place of residence, matter.

The analysis of the contestants’ behavior in the pre-play shows that players make their voting

decision dependent on objective criteria such as their opponent’s monetary contribution to the

stake size as well as on subjective criteria such as the player’s trustworthiness and race. In

addition, we observe that the weight given to objective and subjective criteria changes between

the ﬁrst and the second voting decision. In the second round, apart from stake size, player’s

trustworthiness seems to be more important than player’s demographics. Further, we show that

there is a strong link between the two rounds of pre-prisoner’s dilemma play and the player’s

decision on cooperation. For instance, we ﬁnd that whether a player lied about her stakes in the

pre-play has a signiﬁcant eﬀect on the cooperation rate.

While writing the ﬁrst draft of this paper, it came to our attention that van den Assem et

al. (2010) are simultaneously analyzing data from “Golden Balls”. Both studies are conducted

independently of each other. The only overlap is in the analysis of unilateral cooperation in

the ﬁnal round. As we mentioned, we also extensively analyze the pre-play with respect to its

inﬂuence on the outcome of the prisoner’s dilemma game, and we also include variables describ-

ing communication, e.g., whether players shake hands or promise each other to cooperate. In

addition, the data set used in the two studies diﬀers with regard to the deﬁnition of player’s

demographic characteristics and the construction of explanatory variables such as reputation or

reciprocity. Therefore our analysis and results diﬀer in various aspects.

The structure of the paper is organized as follows. We start with a brief review of the re-

lated literature, section 2, followed by a description of the game show and data set, section 3.

In section 4 we explain the strategic considerations of the players and motivate our analysis.

Sections 5 and 6 represent the main part of the paper, including the empirical analysis and ob-

tained results on cooperative behavior in the prisoner’s dilemma as well as contestants’ pre-play

voting behavior. Section 7 concludes.

2 Literature review

In this section, we ﬁrst review studies that are closely related to our paper in terms of using

television show data and/or in terms of considering a prisoner’s dilemma with defection being

the weakly dominant strategy. Secondly, we present studies analyzing the eﬀect of stake-size,

anonymity, communication, and gestures on cooperative behavior in social dilemma games.

Finally, we give a brief overview of results about lying and discrimination in voting decisions.

Television game shows and weak prisoner’s dilemma

Related studies that use television game show data are provided by List (2006), Oberholzer-Gee

et al. (2010), and Belot et al. (2010). The ﬁrst two analyze “Friend or Foe”, a US game show,

and the latter analyzes “Will (s)he share or not?”, a show from the Netherlands. In both shows

pairs of players build a jackpot by answering trivia questions together. The teams have to decide

about the division of their accumulated jackpot by playing a prisoner’s dilemma with weakly

dominant strategies. In contrast, in “Golden Balls” stakes are built by a random process and the

two ﬁnal players are selected on the basis of a two-round voting procedure. Thus, the process of

building the stakes and the pre-play partner selection is rather diﬀerent. In addition, “Golden

Balls” provides the opportunity to analyze a game with very high stakes, i.e., the average jackpot

is more than three times as high as the average jackpot in “Friend or Foe” and its median value

is more than three times the median in “Will (s)he share or not”. All three studies ﬁnd a very

high cooperation rate (around 50%), but only Belot et al. (2010) ﬁnd a none-negligible eﬀect of

the stake size.

Little empirical work has been done on cooperation in prisoner’s dilemma games in which defec-

tion is a weakly dominant strategy.

The only studies we are aware of are Ortmann and Tichy

(1999) and studies related to the work of Rapoport on social dilemmas. Ortmann and Tichy

(1999) analyze the game with respect to gender diﬀerences. They ﬁnd an overall cooperation

rate of 46%, and that females cooperate more frequently than males. The latter studies analyze

the game with respect to the inﬂuence of “fear” and “greed” on the cooperation rate.

The exper-

iments show that the cooperation rate is higher in a prisoner’s dilemma with weakly dominant

strategies than in one with strictly dominant strategies.

Stake size, anonymity, and communication

The eﬀect of the stake size on cooperation rates in dilemma games is widely debated and no

clear answer has been found so far. Some experiments show that there is no signiﬁcant eﬀect,

whereas others suggest that the cooperation or contribution rate decreases with the stake size.

Compared to experiments in the laboratory, contestants in “Golden Balls” do not anonymously

play the prisoner’s dilemma and are allowed to communicate with each other before choosing

their action. The relevance of anonymity in dictator games is shown by Hoﬀman et al. (1994). If

people feel observed by the experimenters they are more altruistic than in a double-blind setting.

In addition, Rege and Telle (2004) showed that the framing of the instructions of the game may

raise the cooperation or contribution rate. Since the players in the game under consideration

are ﬁlmed and play in front of a large television audience, we can expect a similar eﬀect, i.e., a

positive eﬀect on cooperation. The cooperation rate we observe is, however, not much diﬀerent

to the rate reported by Ortmann and Tichy (1999), which might suggest that the eﬀect of the

There is a vast experimental literature on prisoner’s dilemma games in which defection is a strictly dominant

strategy. The cooperation rate found varies between 30-40%, see, e.g., Shaﬁr and Tversky (1992).

Rapoport (1988) introduced these two concepts in order to provide a meaningful interpretation of the payoﬀ

diﬀerences between the unilateral defector’s and the mutual cooperator’s payoﬀ (b= greed) and between the mutual

defector’s and unilateral cooperator’s payoﬀ ( b= fear). Rapoport ﬁnds that the cooperation rate in a prisoner’s

dilemma without fear is higher than in one with fear and predicts a cooperation rate of 50% for a no-fear dilemma

that corresponds to the game analyzed in this paper. The prediction is independent of the stake size. Rapoport’s

ﬁndings are supported in experiments conducted by Ahn et al. (2001) as well as Ahn et al. (2003).

For a comprehensive survey refer to, e.g., Camerer and Hogarth (1999).

audience is not as strong as expected.

In addition, experimental studies have shown that communication increases the cooperation rate

signiﬁcantly (for surveys see Sally (1995) and Ledyard (1995)), although from a theoretical point

of view communication is cheap talk (see e.g., Crawford (1998) and Farrell and Rabin (1996)).

Dawes et al. (1977) have shown that face-to-face communication only has an additional eﬀect on

behavior if the subjects are allowed to discuss the game and the strategy they intend to play. If

they only have the chance to get to know each other, an eﬀect on the cooperation rate is almost

not present. Bohnet and Frey (1999) extend the analysis of face-to-face eﬀects on cooperative

behavior and ﬁnd that merely “seeing” each other’s face without the possibility of communica-

tion, increases the cooperation rate, but that face-to-face communication has a stronger eﬀect,

it rises the unilateral cooperation rate up to 78%.

Furthermore, studies have shown that the eﬀectiveness of communication diﬀers by the words

that are used, for instance, when making a promise. Vanberg (2008) ﬁnds that people have a

preference for keeping a promise and are not driven by concerns about their expected payoﬀ.

Another reason for observing an eﬀect of the word “promise” follows from the work of Ellingsen

and Johannesson (2004) who propose that people have a preference for keeping their word per

se. In contrast, Charness and Dufwenberg (2006) develop the idea that people keep promises

because of guilt aversion.

Investigating the eﬀect of how a promise is made within face-to-face

communication, either voluntarily or elicited, Belot et al. (2010) ﬁnd that players are roughly

50% more likely to cooperate if they made a voluntary promise to share.

Apart from communication, physical contact, or gestures, i.e., handshakes or hugs, between

players might have an impact on cooperation. To our knowledge there exists no experimental

literature analyzing the eﬀect of a handshake on the cooperation rate. Manzini et al. (2009)

address the issue in the minimum eﬀort game and test whether people’s propensity to choose

high eﬀort is increased if subjects can send a “smile” to the other player instead of pressing an

ordinary “ready to play” button. They ﬁnd that this simple device helps players to coordinate

on a higher eﬀort even though players are not able to see or to talk to each other.

Lying and voting behavior

As already mentioned above, guilt is experienced by subjects if they do not keep a promise

or in other words lied about their intention which strategy they plan to play. Why and when

In laboratory experiments free-form written communication is often used instead of face-to-face verbal com-

munication to be able to disentangle the eﬀect of facial expressions from the bare content of communication. Roth

(1995) provides a survey of bargaining experiments in which the eﬀect of face-to-face communication is tested.

The results suggest that face-to-face communication increases the chance of reaching an agreement even further

than free-form messaging.

In related work, Miettinen and Suetens (2008) show that players feel most guilty if they communicated their

intention to cooperate, but then defected while the opponent cooperated. Charness and Dufwenberg (2010),

however, show that providing subjects merely the possibility of communication by sending the word promise or

not has almost no positive eﬀect on the cooperation rate in a trust game.

people are lying is a further question of high research interest. Gneezy (2005) uses a cheap talk

sender-receiver game and shows that people’s evaluation of whether to lie or not in a situation

depends on the consequences of the lie in terms of payoﬀs. Thereby not only gains achievable

through lying are considered but also possible losses that might occur to the other players. The

fraction of liars is largest if the resulting gains are high and the costs, i.e., losses for the other

players, are low. If players have the opportunity to costly punish the other subjects for playing

selﬁshly, they punish much more often if the selﬁsh action followed a deceptive message (Brandts

and Charness (2003)). Another approach to analyzing lying is made by Fischbacher and Heusi

(2008) who try to ﬁgure out under which circumstances people lie the most. They ﬁnd that

the proportion of truthful, partially truthful and untruthful people is more or less the same

independent of the stake size, the consequences of lying, learning, and the degree of anonymity.

Finally, the partner selection process taking place during the two pre-play rounds in “Golden

Balls” draws our attention to the literature on discrimination. A vast economic as well as psy-

chological literature investigates racial and gender discrimination, but usually with the focus

on the labor market. Two leading theories of discrimination have evolved, taste-based (Becker

(1957)) and information-based discrimination (e.g., Anderson and Haupert (1999)). A common

ﬁnding is that individuals display “in-group biases” in the sense that they favor members of their

own group (i.e., Turner and Brown (1978)).

Related to the pre-play in “Golden Balls”, which involves the elimination of one contestant in

each round in a voting process, are studies using television game show data from the US show

“The Weakest Link”. These analyze discrimination in contestant’s voting decisions in this show.

Levitt (2004) and Anonovics et al. (2005) test taste-based and information-based theories of

discrimination, determining whether contestants discriminate on the basis of gender, age, race,

and skill level. While Levitt (2004) ﬁnds some patterns consistent with information-based dis-

crimination and taste-based discrimination against older players, Anonovics et al. (2005) reveal

taste-based discrimination by women against men. Haan et al. (2002) also use data from “The

Weakest Link”, but analyze whether players make the optimal voting decisions with respect to

maximizing their monetary gains. They ﬁnd that contestants do not use the optimal strategy.

To summarize, there are various reasons to observe a diﬀerent cooperation rate than the one

predicted by game theory and the one observed in laboratory experiments without communi-

cation and high stakes. Based on the facts provided by the literature, we try to shed light on

the factors that determine (non-)cooperative behavior in a prisoner’s dilemma with a weakly

dominant strategy following two rounds of pre-play.

3 Game show and data set

In this section we describe in detail the course of events in the game show (section 3.1) and the

data set we use for the analysis (section 3.2).

For a comprehensive survey on empirical ﬁndings on discrimination refer to Altonji and Blank (1999).

3.1 Structure of the game show

The game show“Golden Balls” consists of three rounds of play with the ﬁnal round being divided

into two phases.

Round 1

The game show starts with four players, usually two women and two men, who are brieﬂy intro-

duced by the show host, i.e., the players provide some information about themselves including

their names, occupation and place of residence.

Then the ﬁrst round starts: 12 golden balls are

drawn from a lottery and four “killer” balls are added, i.e., inside the balls there is written either

a cash amount (in £) or the word “killer”. Killer balls are the worst for the players, because

these may damage the jackpot in the ﬁnal round. The lottery contains 100 golden balls, which

the players have only limited information about. They only know that there may be doubles

and they know the margins of the distribution, i.e., the lottery always contains a minimum ball

value of £10 and a maximum ball value of £75,000. But players do not know the distribution

of the remaining 98 balls.

The 16 balls are mixed and each player is assigned four balls at random. Each player arranges

the closed balls in two rows in front of herself, with two balls on the front and two on the back

row. The two balls on the front row are successively opened by each player, and the revealed

cash values or number of killers is common knowledge to each player. The content of the re-

maining two balls is private information to each player. The players are allowed to secretly look

inside but then have to close the balls again. Afterwards the show host asks each player to state

what is inside their hidden balls on the back row. The order in which players are asked for

their statements is exogenously determined by the show host. Some time for discussion follows,

in which the players express their distrust about each other’s statements. The discussion ends

with each player secretly casting a vote against one of the other players. On the basis of the

votes, a player is eliminated from the show.

After the player who has to leave is determined,

all players open their hidden back row balls and thereby reveal whether they stated the truth

or not. Finally, the four balls of the leaving player are out of the game, while the remaining 12

are carried over to round 2.

Round 2

At the beginning of the second round, two new cash balls are drawn from the lottery and one

killer ball is added. These three new balls are mixed with the remaining 12 from round 1, and are

equally distributed to the three players at random. Hence, there are at most ﬁve killers among

the 15 balls. Again the closed balls are arranged in two rows by each player, i.e., two balls are

on the front and three balls are on the back row. The two balls on the front row are opened

by the players, i.e., their values are common knowledge. The players privately take a look into

Endemol UK ensured us that the four players do not know each other before the show, i.e., they enter the

television studio separately.

The player who receives the highest number of votes has to leave the show. In case of a tie the players having

received no vote can decide which player has to leave. If all players received one vote each, players discuss openly

which player has to leave. If players do not reach a conclusion, ties are broken arbitrarily.

their three back row balls and get the chance to make a statement about their content. This

time the players determine the order of making statements themselves. Like in the ﬁrst round,

the players then get some time for discussion and afterwards secretly choose a player they want

to vote oﬀ.

After the player to leave has been determined all ball values are revealed, the ﬁve

balls of the leaving player are out of the game, and the ﬁnal two players are identiﬁed.

Final Round

The 10 balls from round 2 are carried over to the ﬁnal round and one last killer ball is added.

The maximal amount the players can gain is the sum of the highest ﬁve cash values out of the

11 balls. This amount is called the potential jackpot and its size is always announced by the

show host.

First phase

In the ﬁrst phase of the ﬁnal round the two players successively select ﬁve of the 11 mixed and

closed balls, and these ﬁve values build the jackpot. The player who brought the highest amount

of money from round 2 to the ﬁnal round starts to select one of the balls to “bin”, i.e., to be

taken out of the game, and then chooses one ball to “win”. The balls are not opened until they

have been chosen. Then it is the other player’s turn and vice versa until ﬁve balls have been

selected for the jackpot. If a player chooses a killer ball for the jackpot the accumulated amount

up to that point is reduced to one-tenth of the original value.

Second phase

In the second phase of the ﬁnal round the players play a prisoner’s dilemma in which defection

is a weakly dominant strategy (see table 1).

Table 1: Weak prisoner’s dilemma

Split (C) Steal (D)

Split (C)

J ,

J 0 , J

Steal (D) J , 0 0 , 0

C b= Cooperation, D b= Defection

Such a prisoner’s dilemma has three pure-strategy Nash equilibria, namely (steal, split), (steal,

steal), and (split, steal).

Thus, each player has an incentive to defect, because she is never

monetarily worse oﬀ when doing so. Before the players have to decide which strategy to play,

Again, the player with the highest number of votes has to leave the show, and ties are broken in the same

way as in the ﬁrst round.

The show host explains the diﬀerent outcomes of the game in each episode with the same neutral words, but

does not suggest that one of the options is better or worse than the other (for the exact wording see appendix A).

Two of the resulting Nash equilibria involve one player to cooperate. Applying the method of iterated

elimination of weakly dominant strategies, however, leaves only the (steal, steal) equilibrium, which should be the

only one observed.

they get some additional time, roughly 30 seconds, to discuss with each other what they are

going to do. In the discussion the players try to credibly state that they want to share the

jackpot, i.e., choose to split.

The dilemma game is played as follows: Each player is assigned two balls, one with the word

“steal” and one with the word “split” inside. Then both players choose one of the balls and open

them simultaneously. If both players chose the split ball, the jackpot (J) is divided equally

between the two players. If one player chooses steal and the other chooses split, the former gets

the whole jackpot and the latter receives nothing. If both chose steal, both get nothing

3.2 Data description

“Golden balls” was ﬁrst aired on June, 18th 2007 as a late afternoon (5pm) game show. The

show is still running today and reaches up to 2.2 million people per episode which corresponds

to a market share of 21%.

In total, we have records of 222 episodes, with 203 regular and 19 special episodes. In the special

episodes there are either (i) only players that have “lost” on the show before or (ii) four female

or male players. The regular episodes always consist of two women and two men and all players

are on the show for the ﬁrst time. Importantly, the ﬁrst series (40 episodes) was ﬁlmed prior

to the show’s television premiere. Hence, all players in these episodes had no chance to observe

others playing the show. All later episodes were ﬁlmed after the broadcast of the ﬁrst series.

For all episodes, we recorded variables describing the players (occupation, hometown, gender,

race, and age) and the game (all true and stated ball values in rounds 1 and 2, the order

of making statements in both rounds, votes the players received and submitted, the potential

jackpot size, values of binned balls by each player, the player’s intended strategy

, the jackpot

size, interactions of players before and in the ﬁnal (handshakes, promises), and the ﬁnal decision).

Tables 8 and 9 in the appendix provide an overview of the data.

4 Strategic considerations of the players

Following the structure of the game show, we analyze the player’s incentives to behave in a

particular way. The ﬁnal goal of each player has to be reaching the ﬁnal round with a jackpot

as high as possible and, most importantly, facing a player who intends to split, independently of

whether the player herself prefers to steal or split. Thus, the players have to trade oﬀ these goals

against each other: Players need (i) to get to the ﬁnal round, (ii) to select the “right” opponent,

and (iii) to accumulate as much cash as possible for the jackpot.

Endemol UK ensured us that the players leave the show separately and thus cannot make any further ar-

rangements.

“ITV strikes teatime gold”, guardian.co.uk, July, 3rd 2007.

Before the show starts, the players are individually and privately asked to explain which strategy they intend

to play in the ﬁnal. The recorded statement is only broadcasted to the television audience but not to the other

players or the audience in the television studio.

In the pre-play, players base each of their two voting decisions on exogenous as well as endoge-

nous criteria. We deﬁne exogenous criteria as characteristics of the players that are determined

previously to the show, e.g., the player’s age, gender, race, or place of residence. In contrast,

endogenous criteria evolve during the course of the game, and are, for instance, the ball values

dealt to the players, the order of making statements in round 2, or whether a player lied or not.

The latter criteria can be strategically inﬂuenced by the players. On the one hand, they can try

to behave in a certain way to signal, for example, trustworthiness. Players can decide whether

to lie or not about the content of their hidden back row balls and if so, to what extent, e.g.,

they can conceal a killer or overstate the amount of a cash value. Furthermore, in round 2 they

can decide when to make their statement about their back row balls. Going ﬁrst potentially

inﬂuences other players’ statements.

On the other hand they can try to inﬂuence the other

players’ strategy. During the discussions in round 1 and 2, they can, for instance, state why

they distrust a certain player and try to convince the other players to vote this player oﬀ.

Once players reach the ﬁnal round, they have to make sure that their opponent chooses the split

ball in the ﬁnal decision. Players use the discussion in the ﬁnal round to reassure the opponent

that they will cooperate, e.g., players promise each other to share the jackpot and/or shake

hands on sharing it.

To summarize, the ﬁnal decision as well as the voting decisions are functions of exogenous

personal and endogenous characteristics of the players. Unfortunately, a game-theoretic analysis

of the game is not feasible because the game is too complex and strategies are ill-deﬁned.

However, we will use the logic of backward induction to analyze the decisions made in the

game. Therefore we start with analyzing the decision in the ﬁnal round and then successively

analyze the voting decisions made in round 2 and 1.

5 Analysis of cooperative behavior in the PD

In this section we identify the inﬂuencing factors of cooperative behavior. We observe an average

cooperation rate of 54.5%, which is higher than the one found in weak prisoner’s dilemma ex-

periments without communication, pre-play, and high stakes (e.g., Ortmann and Tichy (1999)).

The rate is also slightly higher than the one observed in “Friend or Foe”, another television game

show experiment, (e.g., List (2006)). Further, we observe mutual cooperation in 33.3% and

successful defection in 42.3% of the cases. Unilateral defectors take home three times as much

money as mutual cooperators, £15,693 versus £4,784, and the average amount of money left on

the table due to mutual defection is £14,426. Altogether 108 players left £1,558,045 on the table.

We will start the analysis in section 5.1 with a discussion of the data and the variables that may

have an inﬂuence on cooperative behavior. In section 5.2 we will test the derived hypotheses in

an empirical analysis. In addition we brieﬂy present an alternative approach in section B.

For instance when the ﬁrst player states high ball values, one is inclined to state a high value as well and

thereby might tell a lie. In addition, in round 2, stating to have one of the two new balls, which are added in that

round, might distract the other players from a worse front row.

5.1 Possible determinants of coop erative behavior

As we already pointed out in section 2, the prisoner’s dilemma under consideration is diﬀerent in

various aspects from the ones usually analyzed in the literature. In this section we will discuss

the potential impact of those diﬀerences on the observed degree of cooperation, and present

ﬁrst results. The section is divided into four parts that correspond to the groups in which the

variables are presented in the regression tables in section 5.2, (i) player characteristics, (ii) stake

size, (iii) communication, and (iv) pre-play.

(i) Player characteristics

In this category we discuss variables that are exogenously determined. These are demographic

player characteristics

and a variable expressing the player’s experience in the show.

Experience We deﬁne the players of the ﬁrst 40 episodes (series 1) as unexperienced players.

They had no chance to observe other contestants playing the game. In contrast, all later episodes

have been ﬁlmed after the television premiere of “Golden Balls”. Thus one could conjecture

that the experienced players are better in assessing whether cooperation or defection could be

successful or not. But from the raw data, we do not observe a substantial diﬀerence, neither in

the cooperation rate nor in the distribution of outcomes (see tables 10 and 11 in the appendix).

A binomial probability test

can neither reject the null hypothesis of no diﬀerence between the

cooperation rate of experienced and unexperienced players (p=0.372), nor the null hypothesis of

no diﬀerence between the probability of mutual cooperation of experienced and unexperienced

players (p=0.481).

Demographics Player’s demographics are deﬁned as exogenous characteristics of a player

such as gender, age, race, place of residence, or occupation (descriptive results are reported in

tables 10 and 11 in the appendix). The relation between demographic characteristics and social

behavior seems to be rather ambiguous. Deriving clear-cut hypotheses about the inﬂuence of

these characteristics on the player’s propensity to cooperate is therefore not possible.

Overall, there seems to be no diﬀerence between the cooperation rates of men and women.

Concerning the rate of successful cooperation we ﬁnd that it is lowest for female teams (28.6%)

and highest for mixed gender teams (35.3%). The null hypothesis of no diﬀerence between the

overall cooperation rate of men and women cannot be rejected (p=0.435) as well as the one

for the mutual cooperation rate (p=0.503). Players above the age of 40 cooperate signiﬁcantly

more than players below 40 (p=0.001). There are only small diﬀerences in the success rates of

cooperation, teams of players below 40 have the lowest success rate. Whites are more likely to

We also use the player-characteristics to construct variables describing opponent- and team-characteristics.

This result is in contrast to the ﬁnding of Oberholzer-Gee et al. (2010) who ﬁnd an eﬀect of learning for

players in later episodes of “Friend or Foe”.

All tests used in this paper are two-sided binomial probability tests, unless stated otherwise.

However, gender conditional on age tends to have an eﬀect on the cooperation rate, i.e., women below 40

cooperate more than men below 40 and vice versa for men and women over 40. Note, the results concerning age

should not be attached too much weight since the age categories are merely assessed by personal judgment.

cooperate compared to non-whites, but the diﬀerence is not signiﬁcant (p=0.334).

A much stronger eﬀect than the one of age, race and gender, seems to be the eﬀect of whether

a player’s place of residence is England or another part of Great Britain.

Players living in

England cooperate signiﬁcantly less than players from other parts (p=0.000). In addition, if

neither player lives in England the success rate of cooperation is 50.0% versus 32.5% if both

players live in England, and 33.3% if it is a mixed team. The failure rate is highest for mixed

teams and signiﬁcantly higher than the one of English teams (p=0.002).

Further, decisions made in the game might have implications beyond their immediate conse-

quences, because the game is played in front of a large television audience and is therefore pos-

sibly being watched by friends, family members and/ or colleagues. Depending on the player’s

occupation, it can be in her interest to appear trustworthy. For instance, police oﬃcers act as

role models for observing the law and behaving correctly, or teachers are responsible for a moral

education of children. These players have an incentive to behave in a fair way, especially when

it comes to choosing the strategy in the prisoner’s dilemma. We identify roughly 15% of contes-

tants with an occupation for which their reputation is a valuable asset, and construct a variable

“social job”, including e.g., priests, policemen, ﬁremen, childminders, and teachers. Having a

social job might inﬂuence cooperative behavior because of two diﬀerent reasons. On the one

hand, players with a social job could be more cooperative because they want to show that they

behave socially responsible. On the other hand, the causality could be vice versa: Having a

social job could be a sign for being a cooperator itself, because a cooperative person chooses

a job in which she can behave according to her preferences. In that case cooperative behavior

would not be driven by the opportunity to appear trustworthy. Summarizing, it remains unclear

whether we will observe an eﬀect of having a social job.

Social closeness The sociological literature argues that the degree of similarity between play-

ers has an impact on their social interactions. While some people might be willing to cooperate

without discrimination, others are highly suspicious of people who are not like them and prefer

to keep them at arm’s length. In many social networks, e.g., friendships, marriages or busi-

ness relations, one observes that individuals associate disproportionately with others who are

similar to themselves, i.e., people are more likely to form social ties with others who are alike.

This tendency of people to relate to similar types is referred to as “homophily”, ﬁrst deﬁned by

Lazarfeld and Merton (1954).

Such motivated, we construct an index for the closeness between

Furthermore, based on a player’s hometown we construct variables indicating whether the player lives in

London, in a large or a small city (see table 8).

The hypothesis of no diﬀerence between the success rates of not-English and English teams (p=0.284), of

not-English and mixed teams (p=0.454), as well as of English and mixed teams (p=0.849) cannot be rejected.

Neither can the hypothesis of no diﬀerence between the failure rates of not-English and English teams (p=0.495)

and of not-English and mixed teams (p=0.162) be rejected.

For a survey with respect to sociology see Jackson (2008) and with respect to cooperative game theory see

van den Nouweland and Slikker (2001). Homophily is usually based on a variety of characteristics, including

gender, race, age, region and education. Studies analyzing the impact of homophily on behavior make use of a

normalized measure of diﬀerences between the observed mix of friendships and the expected mix if friendships

were formed uniformly at random. It has been shown that personal characteristics have far weaker predictive

power than network attributes in determining strategic behavior. But they play an important role in determining

the outcomes by aﬀecting the social network, and thus the network’s type in terms of the social distance of

players by accounting for players’ age, gender, race, occupational status, and place of residence

(England). The index ranges from 0 to 1, weighting each component by one-ﬁfth.

Concerning

the distribution, we observe the majority of players to have an index-value of either 0.6 (44%)

or 0.8 (32%).

(ii) Stake size

Categorizing the jackpot in ﬁve divisions (see tables 10 and 11 in the appendix), we ﬁnd that

the cooperation rate decreases with a continuous increase in the jackpot size. But, surprisingly,

the rate declines sharply from 73.6% for jackpots below £500 to roughly 50% for jackpots above

£500.

Concerning the mutual cooperation rate, it is signiﬁcantly higher if the two players

face a jackpot below the level of £500 (p=0.000). This result is even more remarkable if one

bears in mind that a stake size around £500 is already much higher than the one used in most

laboratory experiments. At the same time, however, the cooperation rate rises with an increase

in the potential jackpot, i.e., the highest possible jackpot the players could obtain after the ﬁrst

phase of the ﬁnal round. Hence, the eﬀects of the actual and the potential jackpot operate

in opposite directions. One might presume that the players’ perception of the actual jackpot

depends on the potential jackpot, i.e., two actual jackpots equal in size will be judged diﬀerently

depending on their diﬀerence to the potential jackpot. In table 2 we explore this issue further.

We depict the cooperation rate for the ﬁve diﬀerent jackpot categories and within each we split

up the rate by the four categories of the potential jackpot. The diﬀerence between the highest

potential and the actual jackpot is increasing within each category. Fixing the jackpot categories,

we ﬁnd that the cooperation rate almost always increases with the size of the potential jackpot.

This corroborates the idea of a biased jackpot perception, that we will discuss in detail in the

following.

Expectation Players might build an expectation about the size of the actual jackpot depend-

ing on the observed size of the potential jackpot. This expectation is used to judge the size

of the actual jackpot. But, computing the correct expectation is a rather diﬃcult task if no

computer is at hand. Therefore, players need some alternative method to calculate their ex-

pectation. As mentioned before, the ﬁrst 40 episodes have been broadcasted before all other

episodes were ﬁlmed. Henceforth, we assume players to take the observed average ratio between

the jackpot and the potential jackpot in series 1 as an estimate to roughly calculate their expec-

tation. The average jackpot in series 1 is £13,066 which corresponds to 27.5% of the average

potential jackpot of £47,526. This ratio is multiplied by the observed potential jackpot in each

interactions an individual with certain characteristics experiences (McPherson et al. (2001)).

For instance, if both players in the ﬁnal are male, white, have a social job and live in England, the index

takes a value of 0.8, while if both are just male and white it takes a value of 0.4. Currently we reﬁne the index

by looking at peoples’ job-income relationship, which will give us additional variation by player. There we make

use of the socio-economic index for occupational status (Ganzeboom et al. (1992)).

The diﬀerence between the cooperation rate is highly signiﬁcant (p=0.000) taking two categories with the

cutoﬀ of £500.

Table 2: Relation between jackpot and potential jackpot

Jackpot Potential Jackpot Split

in £ in £ Row % N

[3, 500] [5000, 30000] 62.5 32

N=72 (30000, 45000] 85.7 14

(45000, 75000] 75.0 12

(75000, 168100] 85.7 14

(500, 2500] [5000, 30000] 41.2 34

N=100 (30000, 45000] 59.5 42

(45000, 75000] 44.4 18

(75000, 168100] 100.0 6

(2500, 10000] [5000, 30000] 50.0 30

N=102 (30000, 45000] 43.3 30

(45000, 75000] 66.7 18

(75000, 168100] 58.3 24

(10000, 30000] [10000, 30000] 38.9 18

N=116 (30000, 45000] 45.7 46

(45000, 75000] 52.9 34

(75000, 168100] 55.6 18

(30000, 100150] [30000, 45000] 50.0 6

N=54 (45000, 75000] 50.0 22

(75000, 168100] 46.2 26

Note, that the diﬀerence between the jackpot and the potential jackpot is increasing with an

increasing potential jackpot per jackpot category.

episode, and determines the players’ expected jackpot.

Depending on whether the jackpot is

above or below the player’s expectation, the propensity to cooperate changes. The cooperation

rate is signiﬁcantly higher (p=0.002) if the jackpot is below the expectation, and cooperation

is much less successful if the expectation threshold is taken, i.e., 18.4% versus 41.1% of mutual

cooperation.

(iii) Communication

Apart from communication that takes place in round 1 and 2, and in the ﬁrst phase of the

ﬁnal round, players explicitly get some time to discuss the strategy they intend to play in the

prisoner’s dilemma. The players use this time to assure each other their willingness to cooperate,

i.e., to choose the split ball. As described in section 2, studies have shown that especially face-to-

face communication, involving a mutual agreement to cooperate, increases the cooperation rate

signiﬁcantly. We observe that 24.8% of the players voluntarily promise each other to cooperate.

In addition to verbal communication, 39.2% of the players shake hands to corroborate their

intention to split, and 41.4% out of those do both, i.e., they shake hands and promise each other

to share the jackpot. We deﬁne dummy variables to control for mutual promises, handshakes

and for whether the contestant starts the ﬁnal discussion. We expect handshakes and promises

to facilitate successful cooperation.

Note that the ratio between the jackpot and the potential jackpot diﬀers only slightly from the one observed

in the episodes following series 1, there the ratio is 25.7%.

(iv) Pre-play

The next three potential determinants of cooperative behavior evolve within the pre-play.

Lying In connection to communication we address the potential eﬀect of lying on cooperative

behavior. Lying is rather common during the pre-play rounds of the game show and might be

thought of as an inherent part of the game. Players are concerned about maximizing the stake

size, thus having low values or killer balls increases the probability of being voted oﬀ. Driven by

the fear of being eliminated from the game when having “bad” balls, the contestants bluﬀ their

way to the ﬁnal. But a player is revealed as a liar after each round, and might get a reputation

of being not trustworthy, which possibly prevents her from lying. Analyzing our raw data, we

ﬁnd that 43% of the players who reach the ﬁnal lied about the content of their balls in round 1

and 37% in round 2. A possible implication of lying is that a liar may want to repay her “guilt”

and therefore is more tempted to cooperate. But a player facing a liar in the ﬁnal perceives the

liar as untrustworthy per se and thus is less willing to cooperate.

We control for the potential eﬀects of lying by introducing dummy variables for whether the

player or her opponent has lied about a cash value or a killer during the two rounds of pre-play,

since we believe that the perception of concealing a killer may diﬀer from that about overstating

a cash amount.

Kindness In addition, we include variables linked to kindness, experienced kindness, and

its repayment in our analysis. Firstly, we account for the impact of the voting decision on

the behavior of those contestants who remain in the show. After each round of the pre-play,

contestants need to cast a vote against a certain player whom they want to leave the game. It

can happen that a player in the ﬁnal has voted against her opponent during the pre-play.

This

might inﬂuence the player’s behavior in the ﬁnal: A player is less likely to cooperate, since she

expressed her dislike against her. In this respect we construct a dummy variable that identiﬁes

the player who voted against her opponent.

Secondly, we deﬁne a variable termed “should have left the game” in order to investigate whether

a player responds to experienced kindness. The variable is constructed as follows: First we rank

the three players in round 2 with respect to their weighted sum of cash values and killer balls.

The dummy points at the player with the lowest weighted sum. From a purely monetary

perspective, this player should be voted oﬀ the game. But if such a player nevertheless reaches

the ﬁnal round, she is aware of owing her “survival” to her opponent.

In this respect one could

surmise that she is more likely to split the jackpot in order to pay back her survival.

Luck At last, we want to focus on the ﬁrst phase of the ﬁnal round, in which the jackpot is

built by an alternating selection of balls. The player who starts to select the ﬁrst balls to bin

For a comprehensive discussion of the voting behavior refer to section 6.

In order to rank the players we use the ex-post cash-killer-criterion which is described and discussed in detail

in section 6. We assume that a player, who does have the lowest weighted monetary amount is aware of this and

does value her survival. Often the players address their pass to the ﬁnal round during the ﬁnal discussion and

thank their opponent for taken her so far.

and win is the player who brought along the higher sum of cash values, i.e., contributed most to

the potential jackpot. The mean diﬀerence between the player’s contributions is £1,678 without

accounting for the possible damage caused by killer balls. The value of the resulting jackpot is

determined purely at random, but one player might be more lucky than the other, i.e., chooses

higher values or bins more killer balls. We control for those eﬀects, constructing three dummy

variables: One for the player who contributed most to the potential jackpot, one for the player

who selects the highest values, and one for the player who bins most killer balls. The more lucky

player or the player who contributed more to the potential jackpot could feel entitled to a larger

piece of the pie and therefore is less likely to cooperate.

5.2 Regression analysis

In order to explore the individual decision process when playing the prisoner’s dilemma game,

we estimate bivariate probits of the probability that player i chooses split or steal as a function

of own and opponents’ characteristics as well as variables determined in the pre-play (see table

3 and table 12).

Additionally, to analyze team cooperation rates, we estimate ordered probits

(see table 4 and 13). We order the outcomes by coding the team outcome as equaling 0 if

both players choose steal, equaling 1 if one player chooses steal and the other chooses split, and

equaling 2 if both players choose split.

Results for unilateral cooperation

We estimate bivariate probits on the probability that player i chooses split (y = 1), or steal (y =

0) as a non-linear function of exogenous demographic player characteristics, D, and variables

that evolved during the game, G, including a constant and one interaction term, namely the

interaction of “handshakes”, x

, and “promise”, x

The conditional probability that player i

chooses split is

P (y = 1|x

, x

, D, G) = Φ(α + β

+ β

+ Dθ + Gν) = Φ(m),

where α, β, θ, ν are parameters to be estimated, Φ(·) is the standard normal cumulative distri-

bution function, and m denotes the index α + β

+ β

+ Dθ + Gν.

In addition, we estimate the same probits including one additional dummy variable, namely whether player

i “voted against (her) opponent” in the pre-play. We exclude the dummy in our main analysis, since including

it reduces the data set by 55 observations which is due to a voting result of 2:1:1:0 in round 1 or 1:1:1 in round

2 (in these cases it is analytically not possible to trace back the players’ individual voting decision). Except for

the episodes with a tie, the outcome of the voting decision is 2:1:0 in round 2, such that none of the ﬁnal players

received a vote from their opponent. Thus, our control variable only comprises of the voting result in round 1.

Additionally, we only control for the voting decision made by the particular player herself, and not whether this

player received a vote by his opponent in the ﬁnal, since after round 1 the player can only speculate who had

casted a vote against her. In the remaining data set only 18 out of 390 players have casted a vote against her

ﬁnal opponent. Thus, comparing table 3 and 12 we ﬁnd slight changes in the estimation results.

The probit models are built around a latent regression of the form y

∗

= α+β

+β

+Dθ+Gν+ε,

ε ∼ N (0, 1). Given the latent index model, the value of our observed binary variable y is computed according to

the relationship y = 1[y

∗

> 0].

The marginal eﬀect for the k-th independent variable is computed as

∂P (y = 1|x

, x

, D, G)

∂x

= φ(m)β

k = 2, ..., K

where φ(·) is the standard normal density function. The magnitude of the derivative is propor-

tional to φ(m)β

. A change in one of the independent variables results in an eﬀective percentage

change in player i’s likelihood to cooperate.

The estimation results are reported in table 3 and

12 (in the appendix).

Table 3 reports the results of four probit models, which diﬀer with respect to the included vari-

ables in the group of stake size and pre-play. Model (1) and (3) include the continuous variables

jackpot and potential jackpot, while models (2) and (4) include the dummy variable describing

whether the expectation of the resulting jackpot is met or not. In addition to the controls for

personal players’ demographics, stake size, and communication, in models (3) and (4) variables

determined in the pre-play are introduced.

Throughout, addressing demographics, we ﬁnd that age, whether a player lives in England, or

whether both players live in a small city have a signiﬁcant eﬀect on the likelihood to cooperate.

If player i is above the age of 40, she is about 16% more likely to cooperate, i.e., split. But, a

player who lives in England, compared to any other part of Great Britain, is roughly 27% more

likely to be a defector, i.e., steal. Additionally, if both ﬁnal players live in a small city, then

player i’s likelihood to cooperate decreases by up to 14%. All three eﬀects are very robust with

approximately the same magnitude across the four models. The results on players’ gender, race,

and occupational status, however, exhibit no signiﬁcant eﬀects. We also ﬁnd no eﬀect for player

i’s experience, i.e., the control for the ﬁrst series has no signiﬁcant eﬀect, indicating that players

are not able to proﬁt from a learning eﬀect if they could watch the game show on television before.

The results on stake size corroborate our insights gained in section 5.1: As suggested, the higher

the actual jackpot, the less likely player i cooperates; while, the higher the potential jackpot, the

more likely player i cooperates. In addition models (2) and (4) highlight our descriptive ﬁnding

that a player is more willing to cooperate if the actual jackpot is below her expectation, i.e.,

her likelihood to cooperate signiﬁcantly increases by roughly 16%. All eﬀects are independent

of player’s characteristics or communication, and are highly robust.

If x

is a dummy variable, the marginal eﬀect is computed as the discrete diﬀerence

4P (y = 1|x

, x

, D, G)

= Φ(m|x

= 1) − Φ(m|x

= 0), k = 2, ..., K.

Note that the marginal eﬀect of the interacted dummy variable “handshakes” (x

) and “promise” (x

) is equal to

the discrete double diﬀerence

P (y = 1|x

, x

, D, G)

= Φ(m) − Φ(β

+ α + Dθ + Gν) − Φ(β

+ α + Dθ + Gν) + Φ(α + Dθ + Gν).

Table 3: Results from binary probit on unilateral cooperation (1)

y = 1 (Split) Marginal Eﬀects

Model (1) Model (2) Model (3) Model (4)

Player Characteristics

Unexperienced -0.028 (0.069) -0.050 (0.069) -0.019 (0.074) -0.041 (0.073)

Male -0.018 (0.059) -0.017 (0.058) -0.019 (0.060) -0.018 (0.060)

Age (>40) 0.164*** (0.064) 0.161** (0.063) 0.174*** (0.066) 0.172*** (0.065)

White 0.117 (0.148) 0.113 (0.145) 0.052 (0.147) 0.046 (0.143)

England -0.269*** (0.078) -0.267*** (0.077) -0.274*** (0.082) -0.271*** (0.081)

London 0.001 (0.103) 0.003 (0.100) -0.059 (0.107) -0.066 (0.104)

Large City -0.054 (0.077) -0.051 (0.075) -0.024 (0.081) -0.018 (0.080)

Student -0.009 (0.096) 0.001 (0.095) -0.020 (0.095) -0.014 (0.095)

Pensioner -0.143 (0.160) -0.160 (0.163) -0.126 (0.164) -0.145 (0.167)

Social Job (Reputation) -0.017 (0.087) -0.032 (0.087) -0.016 (0.090) -0.033 (0.090)

Team Characteristics

Index (Social Closeness) 0.458 (0.309) 0.469 (0.306) 0.592* (0.322) 0.606* (0.318)

Team Male -0.147 (0.099) -0.152 (0.097) -0.183* (0.100) -0.184* (0.097)

Team Female -0.054 (0.095) -0.058 (0.095) -0.083 (0.097) -0.084 (0.097)

Team Age> 40 -0.011 (0.103) -0.009 (0.103) -0.007 (0.106) -0.001 (0.107)

Team Age< 40 -0.049 (0.091) -0.055 (0.090) -0.073 (0.095) -0.075 (0.093)

Team White -0.118 (0.122) -0.124 (0.118) -0.108 (0.124) -0.116 (0.121)

Team England -0.019 (0.093) -0.001 (0.093) -0.021 (0.097) -0.002 (0.096)

Team Large City -0.127 (0.101) -0.128 (0.100) -0.147 (0.101) -0.145 (0.101)

Team Small City -0.141** (0.067) -0.127* (0.067) -0.143** (0.069) -0.126* (0.068)

Opponent Characteristics

Opp. Student 0.087 (0.097) 0.095 (0.095) 0.107 (0.098) 0.111 (0.097)

Opp. Pensioner 0.067 (0.162) 0.049 (0.159) 0.053 (0.171) 0.032 (0.168)

Opp. Social Job 0.040 (0.085) 0.027 (0.085) 0.087 (0.086) 0.073 (0.086)

Stake Size

log(Jackpot) -0.057*** (0.014) -0.057*** (0.015)

log(Pot. Jackpot) 0.097** (0.048) 0.077 (0.050)

Jackpot < Expectation 0.162*** (0.056) 0.173*** (0.059)

Communication

Started Discussion -0.008 (0.048) -0.009 (0.047) -0.005 (0.049) -0.006 (0.049)

Handshakes -0.151** (0.067) -0.179*** (0.066) -0.167** (0.068) -0.196*** (0.067)

Promise -0.032 (0.108) -0.063 (0.107) -0.060 (0.109) -0.095 (0.108)

Handshakes*Promise

0.281** (0.139) 0.309** (0.170) 0.339** (0.142) 0.372*** (0.054)

Pre-play

Acc. Most Money -0.098* (0.058) -0.099* (0.057)

Selected Higher Values in Bin/Win -0.148* (0.079) -0.157** (0.077)

Binned Most Killers in Bin/Win -0.091 (0.090) -0.092 (0.088)

Lied About Cash Value -0.105* (0.059) -0.106* (0.059)

Lied About Killer -0.018 (0.055) -0.017 (0.055)

Opp. Lied About Cash Value 0.019 (0.058) 0.014 (0.058)

Opp. Lied About Killer -0.048 (0.056) -0.041 (0.055)

“Should Have Left The Game” 0.133** (0.062) 0.144** (0.061)

Wald X

61.23*** 55.18*** 74.06*** 69.14***

Log-Likelihood -273.26 -277.81 -264.75 -268.63

Pseudo R

0.10 0.09 0.13 0.11

N 441 441 440 440

Number of Clusters 222 222 222 222

standard errors in parentheses are corrected for episode clusters; * p < 0.10, ** p < 0.05, *** p < 0.01

The marginal for the k-th independent variable is computed as

∂P (y=1|x

,D,G)

∂x

= φ(m)β

k = 2, ..., K.

Team variables are dichotomous (equal 1 if both team members have the same characteristics, and 0 otherwise).

The marginal eﬀect of the interacted dummy variables “handshakes” (x

) and “promise” (x

) is computed as the

discrete double diﬀerence:

P (y=1|x

,D,G)

= Φ(m)−Φ(β

+α+Dθ +Gν)−Φ(β

+α+Dθ +Gν)+Φ(α+Dθ+Gν).

Addressing the controls for communication, we ﬁnd that neither starting the ﬁnal discussion

nor voluntarily promising each other to cooperate are signiﬁcant determinants. But, we ﬁnd a

negative eﬀect of hand shaking: If both ﬁnal contestants shake hands during the ﬁnal discussion

to signal their willingness to cooperate, each player actually is more likely to defect. Thus,

handshakes seem to serve as an instrument to manipulate the opponent’s attitude towards co-

operation. Whether shaking hands is perceived diﬀerently depending on a promise made at the

same time, we interact both dummy variables. As the results show, we ﬁnd a positive signiﬁcant

interaction eﬀect: Shaking hands in combination with a promise actually increases the player’s

likelihood to cooperate. We will further explore whether these eﬀects help cooperators to coor-

dinate by looking at team outcomes in the next subsection.

In models (3) and (4) we introduce controls describing pre-play determinants, e.g., whether

player i accumulated the highest amount of money, selected the higher values, binned most

killer balls, lied about her balls’ content, or should have left the game before.

We ﬁnd that both, having accumulated more money as well as having selected the higher values

when building the jackpot, have a negative signiﬁcant impact on the players’ likelihood to coop-

erate. As suggested, a player might feel entitled to a larger piece of the pie, since she contributed

more to the stake size.

Further, we ﬁnd that a lie about a cash value is treated diﬀerently with respect to its inﬂuence

on cooperation. If player i lied about a cash value, she is roughly 10% more likely to defect in

the prisoner’s dilemma, but concealing a killer has no eﬀect, neither does a lie of her opponent.

Regarding the control indicating that player i should have left the game before, player i is

roughly 14% more likely to cooperate. As hypothesized a player who should have been voted oﬀ

the game, but nevertheless made it to the ﬁnal, is likely to pay back the opponents’ conﬁdence.

Besides, the introduction of the pre-play controls results in two additional eﬀects regarding team

characteristics. We ﬁnd that a male player is signiﬁcantly less likely to cooperate with a male

opponent, indicating that men are more competitive when facing the same sex. Another signif-

icant determinant of cooperative behavior is the index of social closeness between players. The

more similar both ﬁnal players are with respect to their age, gender, race, and place of residence,

the more likely player i is to cooperate with her opponent. This ﬁnding suggests, that in-group

biases may be present.

At last, we brieﬂy want to address table 12 in the appendix. The introduction of the dummy

variable for whether player i voted against her ﬁnal opponent in the pre-play rounds, results in

a negative signiﬁcant eﬀect. As suggested, voting against her opponent expresses her dislike and

causes a higher likelihood to defect.

Apart from that eﬀect, the introduction of the control dummy for voting has an impact on the team variables.

Now, a player from a large city, instead of a small city, is less likely to cooperate. But the eﬀect is only signiﬁcant

at the 10%-level. As mentioned before, this eﬀect might be caused by the reduction of the data set.

Results for mutual cooperation

To understand why players arrive at diﬀerent outcomes in the prisoner’s dilemma, we estimate

ordered probit models. We observe the discrete variable y that can take on three values, i.e., it

equals 0 if both players choose steal, it equals 1 if one player chooses steal and the other chooses

split, and it equals 2 if both players choose split.

The boundaries between the three cases

are determined by the threshold (ξ

), which needs to be estimated along with the rest of the

parameters. The probabilities of the three events y = 0; 1; 2 are given by

P (y = 0) = Φ(ξ

− m),

P (y = 1) = Φ(ξ

− m) − Φ(ξ

− m),

P (y = 2) = Φ(m − ξ

where m = α + β

+ β

+ Dθ + Gν. The marginal eﬀect

of d

) for the j−th

response is computed as

∂P (y = j|x

, x

, D, G)

∂x

= [φ(ξ

j−1

− m) − φ(ξ

− m)]β

The results for the three diﬀerent outcomes are presented in table 4 and 13 (in the appendix).

Concerning team characteristics, the results in table 4 show that teams of English players are

more likely to defect. But the more similar both team players are with respect to their age,

gender, race, and place of residence, i.e., the higher the index value, the more likely they man-

age to successfully cooperate. Addressing the division of team by gender, age or having lied in

the pre-play, there are no considerable diﬀerences. The results also highlight the signiﬁcance

of handshakes and promises. Teams that shake hands or promise each other to cooperate, are

The ordered probit is derived from the latent variable model y

∗

= α + β

+ β

+ Dθ + Gν + ε

∼ N (0, 1), which is similar to the latent model that led to the binary probit model above. The relation between

y and the latent variable y

∗

is assumed to be given by

y =







0, if y

∗

< ξ

;

1, if ξ

≤ y

∗

< ξ

;

2, if y

∗

≥ ξ

If d

) is a dummy variable, then the marginal eﬀect is computed as the discrete diﬀerence

4P (y = j|x

, x

, D, G) = P (y = j|(x

, x

, D, G) + 4x

) − P (y = j|(x

, x

, D, G)).

Note that the marginal eﬀects of the variables that are interacted involve the coeﬃcient of the interaction term.

Therefore, the marginal eﬀect of x

(analog for x

) for the j-th response is calculated as

∂P (y = j|x

, x

, D, G)

∂x

= [φ(ξ

j−1

− m) − φ(ξ

− m)](β

+ β

);

and the magnitude of the interaction eﬀect for the j-th response is given by

∂P (y = j|x

, x

, D, G)

∂x

= [φ(ξ

j−1

− m) − φ(ξ

− m)]β

− [φ

(ξ

j−1

− m) − φ

(ξ

− m)](β

+ β

)(β

+ β

where φ

(·) denotes the ﬁrst derivative of the normal density function w.r.t. its argument. Standard errors are

computed by the delta method.

more likely to miscoordinate. In addition, handshakes in combination with a promise increase

the likelihood of mutual cooperation and decrease the one of mutual defection. As the anal-

ysis of the raw data suggests, we ﬁnd a highly signiﬁcant and inverse eﬀect of the actual and

potential jackpot. Both players are 5% more likely to defect when the stakes are large, and

are 6% less likely to cooperate. In contrast, teams are almost 10% more likely to cooperate

when the potential jackpot increases. Table 13 in the appendix supports the discussed ﬁndings,

highlighting that the players’ expectation about the stake size is also a signiﬁcant inﬂuencing

factor of mutual cooperation. If both players’ expectation about the jackpot is above the actual

one, they are 17% more likely to cooperate, but 16% more likely to defect.

Table 4: Results from ordered probit on outcomes in the PD (1)

y = 0; 1; 2 Marginal Eﬀects

Steal/Steal (0) Split/Steal (1) Split/Split (2)

Team Characteristics

Team Unexperienced 0.000 (0.063) 0.000 (0.013) 0.000 (0.077)

Team Male 0.091 (0.089) 0.006 (0.011) -0.097 (0.083)

Team Female 0.010 (0.064) 0.002 (0.012) -0.012 (0.075)

Team > 40 -0.068 (0.065) -0.023 (0.032) 0.091 (0.096)

Team < 40 0.103 (0.066) 0.012 (0.011) -0.115 (0.070)

Team England 0.121** (0.050) 0.041 (0.026) -0.162** (0.071)

Team Small City 0.079 (0.048) 0.016 (0.013) -0.095 (0.058)

Index (Social Closeness) -0.302* (0.162) -0.063 (0.635) 0.364* (0.195)

Pre-Play

Team Never Lied -0.046 (0.059) -0.013 (0.022) 0.059 (0.081)

Team Lying 0.028 (0.053) 0.005 (0.010) -0.033 (0.063)

Communication

Handshakes 0.078 (0.054) 0.016* (0.009) -0.094 (0.058)

Promise -0.081 (0.053) 0.127*** (0.016) 0.098 (0.064)

Handshakes*Promise -0.295** (0.129) 0.029 (0.046) 0.324** (0.137)

Stake Size

log(Jackpot) 0.051*** (0.013) 0.011 (0.107) -0.062*** (0.015)

log(Pot. Jackpot) -0.081* (0.043) -0.017 (0.178) 0.098* (0.051)

Wald X

36.90***

Log-Likelihood -219.55

Pseudo R

0.08

N 54 94 74

Number of Clusters 222

Standard errors in parentheses are corrected for episode clusters; * p < 0.10, ** p < 0.05, *** p < 0.01

Summary We identify various player characteristics (e.g., age, living in England, or social

closeness), stakes size, and communication, as well as pre-play to be signiﬁcant inﬂuencing fac-

tors of unilateral and mutual cooperation. Most noticeable are the eﬀects of stake size and

communication. We ﬁnd a robust and substantial inverse eﬀect of the actual stake size on

cooperation, i.e., the higher the jackpot the more likely players are to defect. Regarding com-

munication, we test for the eﬀect of handshakes and voluntarily stated promises on cooperative

behavior: Players who shake hands are more likely to defect, while handshakes in combination

with a promise are likely to result in cooperation and successful coordination. We are not aware

of any other study having shown similar eﬀects. Both eﬀects are robust and independent of

player characteristics and pre-play determinants.

6 Pre-play decision making: Voting behavior

As the results from the probit regressions suggest, the characteristics of the opponent play a

decisive role for cooperative behavior. Therefore, we draw our attention to the pre-prisoner’s

dilemma play where the selection of the ﬁnalists takes place. Starting with four contestants, each

round one contestant is voted oﬀ by the other contestants, until only two contestants remain.

Hence, each player faces the decision for whom to vote in round 1 and 2. The voting behavior

will be a function of observable characteristics as well as subjective criteria. We want to map

out some considerations that arise in deciding whom to vote oﬀ. Firstly, players have powerful

incentives to vote in a way that maximizes their chance of building up a high jackpot. In that

manner one would like to vote oﬀ the player who has the lowest cash values or most killers. But,

at the same time, players need to evaluate the opponent’s character in view of the ﬁnal round,

i.e., assess her trustworthiness, sympathy or susceptibility to manipulation. Finally, the players

need to vote in a way that increases their chance of survival, thus their optimal action depends

critically on the belief about how other players vote.

In the next three sections we will show how the players balance their voting decision, bearing in

mind the stake size, the opponent’s character and their own survival. In section 6.1, we discuss

the expected voting behavior with the help of three objective evaluation criteria. In section

6.2 we brieﬂy describe the impact of personal player characteristics as well as round-speciﬁc

determinants. Finally, in section 6.3 we empirically test the validity of the objective criteria.

6.1 Objective criteria

Each episode, before the players have to decide against whom to cast a vote, the show host

reminds the players to “keep in the cash, and kick out the killers”. Following this prompt, we

describe the player’s voting decision by means of three objective criteria. Each episode and round

these criteria predict one particular player who should be voted oﬀ. Throughout we assume that

it is a player’s aim to maximize the potential stake size.

The criteria are deﬁned as follows (see table 5): The cash- (CC) and cash-killer-criterion

(CKC) are constructed on the basis of the (weighted) monetary values of balls and declare the

player with the lowest amount of money to be voted to leave the game. While we count a killer

ball as a ball with zero value in the CC, we attach the killer balls a weight of 0.1 in the CKC,

i.e., one killer ball reduces the monetary value to one-tenth of the original value, a second killer

ball reduces it to one-hundredth of the original value and so forth. The killer-criterion (KC)

counts the number of killer balls per player, and accordingly declares the player with the highest

number of killer balls to be voted oﬀ. Here, the total weight lies on the killers and no weight

lies on the values.

Further, within each criterion we distinguish three diﬀerent time-dimensions, i.e., we determine

the prediction of each criterion separately taking into account (i) the two opened balls on the

front row (ex-ante), (ii) the two open balls and the statements of the hidden back row balls

(stated), and (iii) all revealed balls (ex-post

Table 5: Objective criteria and time-dimension

CC KC CKC

ex-ante value of open balls number of killers of

open balls

weighted mix of

values and killers of

open balls

stated ex-ante + stated

values of back row

balls

ex-ante + stated

killers of back row

balls

ex-ante + stated

weighted mix of

back row balls

ex-post ex-ante + true val-

ues of back row

balls

ex-ante + true

killers of back row

balls

ex-ante + true

weighted mix of

back row balls

By means of these three, respectively nine criteria, we analyze to what extent each criterion

explains the player’s voting decision within and between round 1 and 2. Descriptive results are

reported in table 14, 15, and 16 in the appendix.

Table 14 presents proportions of players who are eﬀectively voted oﬀ in line with the three cri-

teria. Focusing on the time-division of each criterion, in round 1 we ﬁnd that most players vote

in line with the prediction of the ex-ante CKC and ex-ante CC, as well as of the stated KC. In

round 2 instead, the ex-post CKC and the ex-post CC dominate, but the stated KC again yields

the best prediction. Overall the KC, especially when looking at the stated values, ﬁts best: In

round 1, 81.1% of players who are voted oﬀ have the highest number of killer balls both on their

front row as well as stated on their hidden back row balls; in round 2 this proportion slightly

reduces to 70.3%, but still exceeds the CC and CKC.

The ﬁndings are conﬁrmed when considering table 15, which separately reports for each crite-

rion the proportions of players who received a vote when predicted. In addition, the results are

distinguished by gender. As above, we focus on the time-dimension of each criterion and ﬁnd

that the players most frequently vote in line with the ex-ante CKC and CC in round 1, but in

line with the ex-post CKC and CC in round 2. Concerning the KC, players vote in line with the

stated KC in round 1 and the ex-ante KC in round 2. Separating these ﬁndings by gender, we

observe that signiﬁcantly more males than females vote in line with the stated KC and ex-ante

CKC in round 1 (p = 0.024 and p = 0.034) whereas in round 2 more females vote in line with

The main reason why we look at the ex-post criteria is to test whether the players use the ex-ante criteria as

a best estimation of the true state.

Note that we exclude those episodes which have a voting result of 2:1:1:0 in round 1 or a tie in round 2,

since it is analytical impossible to reconstruct the players’ individual decision. Additionally, in tables 15 and 16

we restrict the sample to only those players who take part in both rounds (with an almost equal share of males

(48.5%) and females (51.5%)); thereby we can compare the voting results for both rounds taking the same player’s

decisions into account.

the ex-post CC (p = 0.021).

Most noticeable, in both rounds the players take the statements about killer balls seriously,

although one might argue that statements are only cheap talk and should therefore be ignored.

But a statement about a killer ball has to be treated diﬀerent from stating a particular value.

In our setting, players have a strong incentive to lie about a killer ball, since it threatens them

progressing in the game. If players nevertheless state to have one, this message is “self-signaling”

and not cheap talk: If a player states to have a killer ball it is the truth.

A ﬁrst result is that players seem to base their voting decision on objective criteria, but switch

within the time-dimension of the criteria from round 1 to 2. In round 1 the players do not

know the distribution of balls. Only the values of the two revealed front row balls are common

knowledge. Instead in round 2 the players know all remaining values from round 1, thus the

distribution of balls is known and the player’s voting decision is based on more information than

in round 1. Using the statements about the hidden ball values, the players are able to infer -

up to a certain extent - whether a contestant lies. These informational advantage in round 2

explains why players now most frequently vote in line with the ex-post criteria. In what follows

we provide a detailed discussion of this informational separability between players and rounds.

Information based separability of players

As we pointed out above, in the two pre-play rounds the players have diﬀerent information about

the distribution of values. In round 1, the players face a situation in which they base their voting

decision on an ambiguous distribution of outcomes, created by missing relevant information, i.e.,

they do not know the distribution of values on the back row of each opponent. In round 2 the

situation is modiﬁed. After a player is determined to leave the game, all contestants need to

reveal their true values on the back row. The 12 balls carried over from round 1 to round 2

are common knowledge to all remaining contestants, and only the two new added cash values

are unknown. Now, a player can be in two diﬀerent states: First, if both new values are within

the revealed balls on the front row, or a particular player has at least one new value on her

hidden back row and the other is observable on any other player’s front row, she knows the

exact distribution of values in play. From an informational point of view a player who knows all

ball values in play, makes up her voting decision in a situation where only the precise allocation

of each value is uncertain. Second, if both new values remain unobservable, a player again lacks

information, but not as severe as in round 1.

We use the terminology of uncertainty versus

ambiguity to provide a clear-cut distinction between players informational background in round

1 and 2.

Naturally the extent of information about a state’s probability inﬂuences the players’

willingness to bet on the state.

We also analyzed the case when only one of the new ball values is known to a player, termed partial ambiguity

(see table 16). But for the sake of clarity we limit the discussion to the cases when both new values are either

known or not.

Throughout we assume that a player decides against whom to cast a vote being either in an ambiguous or

uncertain state with respect to her informational background about the balls’ values in play.

A large body of literature deals with this pattern; Camerer and Weber (1992) review most important empirical

and theoretical literature on ambiguity in decision making.

We expect that a player, who faces uncertainty about the allocation of balls makes her voting

decision in consideration of all “true” values, and weights the utility of the outcome by the prob-

ability of obtaining it. For those players, the observed eﬀect that players tend to vote by means

of the ex-post criteria should be more pronounced, especially compared to those players who are

in a situation of ambiguity in round 2. Players facing ambiguity should vote most frequently by

means of the ex-ante criteria, especially in round 1.

In round 2, the voting behavior of those

players should only slightly diﬀer within the time-dimension of each criterion.

In what follows we refer to table 16 that presents proportions of the players’ voting decision

by means of the three criteria and its time-divisions. For round 2 the results are separated

between players facing uncertainty or ambiguity. We restrict the data set to compare the same

573 players in round 1 and 2, of which we identify 50 players to be in an uncertain state, and

241 players to be in an ambiguous one in round 2. In round 1 all 573 players are in the same

ambiguous situation.

As suggested, we ﬁnd that the proportion of uncertain players who vote in line with the ex-post

CKC is signiﬁcantly higher (p=0.004 and p=0.000) than of ambiguous players.

Additionally,

the spread between proportions of players who consider the ex-post or the stated prediction

within the CKC is much larger for players facing uncertainty than ambiguity.

This indicates

that those players are able to infer which player overstates her hidden values on the back row,

and in return cast a vote against her.

The KC is again special, ﬁrstly, due to the self-signaling

message when stating a killer ball, and secondly because the number of killer balls seem to be

the strongest determinant for player’s voting behavior.

Summary With the help of the time-dimension within the three criteria we get information

about the decision making of more than two thirds of the players. For these players we can

say that their decision traces back to an objective evaluation of their opponents by giving most

A choice based on maximizing the expected utility is not possible in this situation, and players form a more or

less vague belief about probabilities to weight outcomes. Quantifying the non-probabilistic ambiguity, alternative

approaches sometimes suppose that the decision maker formulates a subjective, though not necessarily Bayesian,

probability for possible outcomes. Underlying lies the psychological assumption that the subjective weights

given to ambiguous probabilities are the outcome of a mental anchoring-and-adjustment process (Tversky and

Kahneman (1982)). Individuals are assumed to anchor on a particular estimate of the probability and then adjust

it via a mental simulation process. In light of the ambiguity in the probabilities of the outcomes, the player is

unable to evaluate a precise expected utility, since the probabilistic information to the decision maker is incomplete

(see e.g., Hogarth and Kunreuther (1992)). Additionally, optimism or pessimism might be an important feature

of a player’s attitude towards ambiguity, by over (under)-weighting the likelihood of good (bad) outcomes (e.g.,

Chateauneuf et al. (2007) and Cohen (1992)).

We test the hypothesis of no diﬀerences between uncertain and ambiguous players for the CKC by comparing

the same 50 players in round 1 and 2.

For instance, in round 2 70% of all player facing uncertainty, vote by means of the stated CKC, but only 55%

of all players in round 1, compared to 64% of players facing ambiguity in round 2. The same holds for the ex-post

CKC, as well as for males and females in both criteria.

Besides we ﬁnd a diﬀerent voting pattern for males and females facing uncertainty: A much larger proportion

of males votes in line with the ex-ante CC and CKC than females in round 2, while these are almost equal when

players are ambiguous, or in round 1.

weight to killer balls. Interestingly, given the predictions of all criteria, we ﬁnd contrary voting

patterns due to informational diﬀerences between both rounds of pre-play, i.e., in round 1 most

players vote in line with the ex-ante criteria, but in line with the ex-post criteria in round 2.

6.2 Subjective criteria and pre-play determinants

Regarding players’ choice of their counterpart for the ﬁnal round, besides the objective criteria,

subjective personal valuations as well as observed behavior in the ﬁrst two rounds are likely to

play a decisive role.

First, it is likely that people have diﬀerent “tastes” for others. We ﬁnd that women are more

likely to vote against men and vice versa. In round 1, males cast a vote against females in 65%

and females against males in even 75%.

In round 2 we ﬁnd that only females are more likely

to cast a vote against males (52%, p = 0, 096), but that males are signiﬁcantly more likely to

vote against their same sex (54%, p = 0, 064). This ﬁnding suggests that in-group biases may be

prevalent, especially in round 1.

Apart from gender diﬀerences, we ﬁnd that non-whites reach

the ﬁnal round signiﬁcantly less frequently: 63% of non-whites do not reach the ﬁnal (p = 0.000).

Second, we ask whether the order in which players announce the content of their hidden balls

impacts on the players’ voting decision. The determination of the order diﬀers between rounds:

In round 1, the show host calls on a particular player to start telling what is on her hidden back

row balls. Usually this is the player with the weakest front row. Thus, in round 1 the order of

statements is exogenously determined by the show host. In round 2 instead it is endogenous.

The show host asks the players who wants to open up the round. On the one hand starting to

report the content of the hidden back row balls helps to state high values, especially if it is the

truth, and thereby turning the focus on the opponents’ balls. On the other hand, the player

who begins to state her hidden values cannot make her statement dependent on her opponents’

statements, e.g., if all other players confess to have a killer ball a player who states her values

afterward might be more likely to confess a killer as well. After round 2, we observe that only

26.1% of the players who announce ﬁrst are eﬀectively voted to leave the game, but the second or

third player is voted oﬀ in 38.7% and 35.1%, respectively.

Therefore, we expect that the order

in round 2 has explanatory content in the sense that a player has a lower propensity to receive

a vote or is less likely voted oﬀ if she makes her statement ﬁrst. In round 1 we do not expect

the order to have additional explanatory power, since the player is either selected randomly or

due to her weak front row. The eﬀect of a weak front row on the likelihood of receiving a vote

is already captured by the objective criteria.

Over the whole sample, we ﬁnd only 22 contestants (2.8%) who do not vote in line with neither criterion, and

only 65 contestants (8.3%) who never vote in line with an ex-ante criterion.

The null hypothesis of no diﬀerences between the shares of men and women who receive a vote from women

or men, respectively, can be rejected (p = 0.000 and p = 0.000).

In addition, we ﬁnd that males receive a vote more frequently than females. In round 1, 55% of males receive

a vote (p = 0.000), in round 2 53% (p = 0.012).

The test for the diﬀerence between the order of statements is highly signiﬁcant between the ﬁrst and second

player (p = 0.000), and the ﬁrst and third player (p = 0.001). There is no diﬀerence between being the second or

third announcer (p = 0.241).

Concluding, we expect that voting incentives switch between rounds: Players are expected

to attach more weight to the objective criteria in round 1, whereas they shift weight from the

objective criteria to personal judgments about opponent’s sympathy or trustworthiness with

regard to the ﬁnal in round 2.

6.3 Regression analysis

In this section we determine which of the objective as well as subjective determinants, explain

the observed voting pattern best and thus aﬀect a player’s survival within the two rounds of pre-

play. Addressing the objective criteria, which we discussed in section 6.1, we construct variables

for each criterion and their corresponding time-dimension. For each criterion the variables are

composed of (i) the sum of the two open balls, (ii) the sum of the stated values on the back row,

and (iii) a dummy indicating whether the player made a truthful statement about her hidden

back row balls or not.

We expect that the values or number of killers in the open balls on a player’s front row aﬀect the

decision about whom to cast a vote against in both rounds. But, the statements of the hidden

back row balls are only considered in the voting decision in round 2, since in round 2 the players

have some information about their possible content. More precisely, the higher the amount of

cash in the two open balls, the more likely a player survives the pre-play, but the more killer

balls a player has, the more likely she is eliminated from the game.

In addition, we control for whether it is a good strategy of players to tell the truth about the

content of their hidden back row balls. Although in round 1 the players have no information

about the distribution of balls in play, an honest player might be able to convince the others

that her statement is true, because she is e.g., not nervous. Further, we control for the eﬀect

of lying by including a dummy “lied in round 1” in the regression for round 2, i.e., the dummy

indicates whether a player lied in round 1. A player who lied in round 1 takes the risk of getting

a reputation of being untrustworthy, which she may suﬀer from in round 2. We observe that a

substantial amount of players lies in round 1 (53%) as well as in round 2 (45%). The average

overstatement is £6,413 in round 1, and £5,069 in round 2.

Concerning the subjective criteria and pre-play determinants (section 6.2), we control for the

eﬀects of players’ age, gender, race, and place of residence as well as the eﬀects of lying and the

order of statements in the regression analysis.

First, we estimate a probit on the likelihood that a player is voted oﬀ the game (see table 6).

Second, in an ordered probit estimation we look at the determinants impacting on the likelihood

a player receives 0,1,2, or 3 votes in round 1 (table 17), and 0,1, or 2 votes in round 2 (table

18). Again, we present marginal eﬀects instead of coeﬃcient estimates.

Table 6: Binary Probits on Voting Behavior in Round 1 and 2

= 1 (player i has to leave the show)

Round 1 Marginal Eﬀects

Model (1) Model (2)

Player Characteristics

Male 0.040 (0.035) 0.040 (0.035)

Age > 40 -0.002 (0.035) -0.004 (0.034)

White -0.117* (0.067) -0.109* (0.066)

England 0.023 (0.044) 0.023 (0.043)

Order of Statements 0.024 (0.042) 0.028 (0.041)

Cash-Criterion (CC)

log(Value Open Balls) -0.031*** (0.011)

log(Value Stated Balls) -0.002 (0.017)

Truthful Statements -0.146*** (0.049)

Killer-Criterion (KC)

No. Killers Open Balls 0.142*** (0.036)

No. Killers Stated Balls 0.040 (0.046)

Truthful Statements -0.091** (0.042)

Cash-Killer-Criterion (CKC)

log(Whgt. Value Open Balls) -0.074*** (0.006)

log(Whgt. Value Stated Balls) -0.003 (0.010)

Truthful Statements -0.068** (0.033)

Wald X

161.47*** 232.20***

Log-Likelihood -360.51 -364.04

Pseudo R

0.24 0.23

N 842 842

Number of clusters 211 211

Round 2 Marginal Eﬀects

Model (1) Model (2)

Player Characteristics

Male 0.027 (0.045) 0.026 (0.044)

Age > 40 0.051 (0.045) 0.055 (0.044)

White -0.123 (0.084) -0.110 (0.082)

England 0.050 (0.049) 0.051 (0.049)

Order of Statements -0.101** (0.046) -0.097** (0.046)

Lied in Round 1 0.057 (0.038) 0.055 (0.038)

Cash-Criterion (CC)

log(Value Open Balls) -0.031*** (0.011)

log(Value Stated Balls) -0.002 (0.017)

Truthful Statements -0.146*** (0.049)

Killer-Criterion (KC)

No. Killers Open Balls 0.052 (0.049)

No. Killers Stated Balls 0.071* (0.040)

Truthful Statements -0.147*** (0.049)

Cash-Killer-Criterion (CKC)

log(Wght. Value Open Balls) -0.034*** (0.008)

log(Wght. Value Stated Balls) -0.020* (0.012)

Truthful Statements -0.191*** (0.041)

Wald X

61.55*** 69.99***

Log-Likelihood -368.25 -367.39

Pseudo R

0.08 0.09

N 631 631

Number of Clusters 211 211

standard errors in parentheses are corrected for episode clusters; * p < 0.10, ** p < 0.05, *** p < 0.01.

Note: 11 special episodes in which all players have the same sex are excluded.

The marginal for the k-th independent variable is computed as

∂P (y

=1|X,P )

∂x

= φ(Xβ + P γ)β

Results

Looking at model (1) and (2) in table 6, we ﬁnd a signiﬁcant race eﬀect in round 1. Non-whites

are voted oﬀ more frequently than whites. In round 2, the race eﬀect disappears. But other

personal player characteristics, as gender, age or place of residence, have no impact on the likeli-

hood that a player is voted oﬀ the game in both rounds. Thus, the gender diﬀerences described

in section 6.2 seem to cancel out each other.

Addressing the order in which players make their statements each round, making a statement

ﬁrst has a signiﬁcant impact on the likelihood to be voted to leave the game in round 2: If a

player decides to state the content of her hidden back row balls ﬁrst, the likelihood to stay in

the game increases by roughly 10%. Thus our hypothesis of making the statement ﬁrst allows

players to credibly state “good” balls, is supported. As suggested, there is no signiﬁcant eﬀect

of the order of statements in round 1.

Apart from that, we ﬁnd no signiﬁcant eﬀect on the probability of being voted oﬀ in round 2 if

a player lied in round 1, independent of the lie’s content (overstatement or concealing a killer).

The variables representing the objective criteria are introduced in models (1) and (2), and have a

strong explanatory power, with the highest R

in model (2).

As expected, concerning the open

ball values on a players’ front row, the higher the cash amount the lower a player’s likelihood to

be voted oﬀ. The reverse it true when addressing killer balls. The higher the number of killer

balls in the open balls, the more likely a player is voted to leave the game. The statements about

the hidden back row balls have no eﬀect in round 1, and in round 2 only a statement about

a killer ball is signiﬁcant. This supports our suggestion that statements about cash values are

meaningless, but that statements about killer balls are taken into account in the players’ voting

decision: Confessing a killer ball increases the likelihood of being voted oﬀ the game. Further,

the variable indicating whether a player stated the truth, either about her hidden back row

cash values or killer balls has a signiﬁcant eﬀect. In both rounds it is worthwhile to be honest,

stating the truth reduces the likelihood to be voted oﬀ by roughly 10%. In round 2, the eﬀect

is even more pronounced, which might be due to the players’ informational advantage about

the ball values in play. Although the players have no information about the distribution of the

hidden ball values in round 1, a player who states the truth seems to be able to signal credibility.

For a more detailed analysis of the voting process, we draw our attention to the results from

the ordered probit estimation, see table 17 and 18. There we can identify the eﬀects on the

number of votes a player receives. Overall, the results provided by the probit estimation above

are conﬁrmed.

In addition, we ﬁnd that whether a player lied in round 1 matters for the

probability of receiving zero or two votes in round 2. A player who lied before receives two votes

6% more likely than a player who made an honest statement.

Model (1) simultaneously controls for the CC and KC, model (2) only for the CKC, since it is a mix between

the other two.

From a psychological perspective, people may recognize a liar with the help of certain body signals, for

instance, avoiding eye contact, sweating, or blushing.

The results on the probability of receiving two or three votes in round 1 or 2 are very similar to the ones from

the probit model on the player’s likelihood to be eﬀectively voted oﬀ. This conﬁrms the results, since receiving

two or three votes (likely) results in the player’s elimination from the game.

Finally, we ﬁnd that all eﬀects are more pronounced in round 2 than in round 1. But, the

explanatory power of both models decreases sharply between both rounds. In round 1, the cash-

and killer-criterion in model (1) explain a 16% higher mass of the variance than in round 2

=0.24 to R

=0.008), and the cash-killer-criterion in model (2) explains a 14% higher mass of

the variance than model (2) in round 2 (R

=0.23 to R

=0.09). This decline serves as a further

indicator for the switch between players’ voting behavior. It is likely that players decide on

whom to vote oﬀ the game by means of sympathy or trustworthiness. Unfortunately, we are not

able to directly control for those eﬀects.

Summary Our conjectures regarding player’s strategy are largely conﬁrmed in the data. As

we expected, in round 1 neither player takes into account the statements about the hidden

back row balls, and only decides on whom to vote by means of the ex-ante criteria. However,

players discriminate against non-whites. On the contrary, in round 2 taste characteristics become

meaningless, but players punish liars, i.e., liars have to bear the danger of being voted oﬀ more

likely. Additionally, a player who decides to state the content of her hidden back row balls ﬁrst

is more likely to survive round 2. Surprisingly, the trustworthiness of players is highly valued in

both rounds. Hence, strategic considerations, such as accumulating a high jackpot and selecting

a cooperator as the ﬁnal opponent, rather than player’s characteristics appear to be the primary

determinants of voting behavior in round 2.

7 Conclusion

In this paper we analyze cooperative behavior in a prisoner’s dilemma game in the presence of

high stakes, communication, and two rounds of pre-play, involving two voting decisions. Using

data from 222 episodes of the British television game show “Golden Balls”, we observe a unilat-

eral cooperation rate of 55% and a mutual cooperation rate of 33%.

Summarizing our main results, we ﬁnd that stake size, communication as well as pre-play have

a signiﬁcant impact on cooperation. Stake size is inversely related to player’s likelihood to coop-

erate, i.e., the higher the jackpot the more likely players are to defect. Further we can show that

player’s expectation about the stake size matters: If the jackpot is above (below) the player’s

expectation, the propensity to cooperate signiﬁcantly decreases (increases), and mutual cooper-

ation is less (more) successful. With respect to communication, certain words and gestures are

more important than others. We test for the eﬀect of handshakes and voluntarily stated mutual

promises, and ﬁnd that players who shake hands are more likely to defect, while handshakes in

combination with a promise are likely to result in cooperation and successful coordination. The

eﬀects of stake size and communication are robust and independent of player characteristics and

pre-play determinants.

The analysis of contestants’ behavior in the pre-play shows that players make their voting deci-

sion dependent on objective criteria, i.e., their monetary contribution to the stake size, as well

as on subjective personal characteristics of their opponents. We show that there is a strong link

between the two rounds of pre-play and the players’ decision in the prisoner’s dilemma. Whether

a player lied in the pre-play or contributed more to the stake size has a negative inﬂuence on

cooperative behavior, whereas whether a player enjoys her opponent’s goodwill has a positive

one.

We are aware that there are potential drawbacks associated with the use of television game

show data. The ﬁrst addresses anonymity: Players on the show interact face-to-face and in front

of large audience, including their family, friends, and colleagues. This might amplify coopera-

tive behavior, e.g., a selﬁsh-person might choose to cooperate only to avoid embarrassment or

punishment by her peer group. The second addresses the selection of players for the show: Con-

testants are not randomly selected, but have to apply to the show. But, with respect to players

exogenous personal characteristics, the sample can be considered, at least to some extent, as

representative of the underlying (British) population.

This paper has shown that decisions in the prisoner’s dilemma are inﬂuenced by the stake size,

the player’s expectation about stakes, and communication. We are not aware of any other study

using handshakes and promises, as well as a player’s expectation about stake size to explain

cooperative behavior.

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Appendix

A Instructions of the prisoner’s dilemma

The show host Jasper Carrott explains the “weak” prisoner’s dilemma in every episode with

almost the same words:

“It is time to split or steal. You have got two ﬁnal golden balls left, you have each

got a golden ball with the word split written inside, you have got each a golden ball

with the word steal written inside. I will ask you to make a conscious choice and you

will choose either the split or the steal ball, neither of you will know what the other

has chosen. If you both choose the split balls, you split today’s jackpot of £J and

you both go home with £J/2. If one of you splits and one of you steals, whoever

steals goes home with all the money £J, whoever splits goes home with nothing. If

you both decide to steal and you are very greedy, you both go home with nothing.

Before I ask you to choose, Player A, B just check the two balls to make sure you

know which is to split and which is to steal. Do not show to each other. It is very

important that you know which is which. [players check the balls] Are you

happy to know which is split and which is steal? Okay, before I ask you to choose,

I will give you some time to talk to each other about what has happened today and

how you feel. [players discuss] Okay, player A, B choose the split or steal ball

now. [players choose balls] Hold it up, make sure that when you open it, the

other player can see it. Player A, B split or steal? [players open balls]”

B An alternative empirical strategy

In section 5, we have shown which factors signiﬁcantly inﬂuence cooperative behavior. In this

section we present an alternative approach by addressing those players who stated their intended

strategy before the game show started. As mentioned in section 3.2, contestants are individually

asked to make a private statement about the strategy they plan to play in case they reach the

ﬁnal round. These ﬁlmed statements are broadcasted to the television audience, but cannot be

observed by the contestants.

We observe an explicit strategy-statement by 59% of the ﬁnal players.

Given these individual

statements, we can infer whether contestants stick to their announced strategy or whether they

deviate. In other words, we look at those players who intended to steal (split) before the show

starts, but at the end choose split (steal). If players are either defectors or cooperators, inde-

pendent of the situation and their opponent, we should neither observe switching strategies nor

signiﬁcant eﬀects of any explanatory variables.

Of course, we cannot verify whether the players are truthfully stating their strategy. But there seems to be

no advantage for a player to lie. Note, that the strategy-statement is not ﬁlmed in the ﬁrst 18 episodes; therefore

the data set is reduced to 204 episodes (408 players).

In table 7 we depict the average cooperation rate for all players and for men and women sepa-

rately depending on their strategy-statement.

Table 7: Relation between commitment and the cooperation rate

All Men Women

Steal (%) Split (%) Split (%) Split (%)

Statement

Steal (N=136) 64.7 35.3 37.3 32.8

Split (N=105) 22.9 77.1 82.2 73.3

Other (N=167) 43.1 56.9 51.4 61.1

Total 45.1 54.9 53.1 56.5

N 184 224 102 122

Interestingly, the raw data show that contestants more often state to steal than to split (136

versus 105 players). But we ﬁnd that players switch their strategy signiﬁcantly more often

(p=0.008) if they initially planned to steal (35.3% split) than if they planned to split (22.9%

steal), and there is no signiﬁcant diﬀerence between males and females. The hypothesis of no

diﬀerence between men and women who initially plan to steal (split) and then split (steal) cannot

be rejected, p=0.590 (p=0.237).

Addressing the players who do not explicitly state their strategy, we ﬁnd that 56.9% actually

split. The diﬀerence between those and the observed average cooperation rate (54,5%) is not

signiﬁcant (p=0.587).

Thus, one could surmise that a substantial fraction of players are of a certain type, either

cooperators or defectors. The ones that change their strategy make their strategy dependent on

the events in the game as well as on opponent characteristics. We therefore can conclude that

at least 17.6% of the players have situation dependent social preferences.

Table 8: Summary statistics, round 1 and 2

Variable Mean SD Min Max N

Occupation

Social Job

(1 = social job) 0.14 0.34 0 1 887

Student (1 = student) 0.08 0.27 0 1 888

Pensioner (1 = retired) 0.03 0.17 0 1 888

Place of residence

England (1 = England, 0 = SCO, WAL, NIR, IRL) 0.85 0.36 0 1 886

Large City

(1 = population > 268,300 ) 0.30 0.46 0 1 886

London (1 = London) 0.13 0.34 0 1 888

Gender, race, and age

Gender (1 = male) 0.50 0.50 0 1 888

Race (1 = white) 0.92 0.27 0 1 888

Age

(1 = above 40) 0.43 0.50 0 1 888

Average cash ball in the show 5619.55 10374.12 10 75000 3108

Strategy statement

(0 = steal, 1 = split, 2 = other) 1.08 0.86 0 2 612

Round 1

Value of open balls (balls 1 and 2)

8802.64 13858.91 0 104000 888

Value claimed for balls 3 and 4 14265.86 13908.53 0 83000 888

Value of closed balls (balls 3 and 4) 7852.88 12315.07 0 83000 888

Number of killers in open balls 0.47 0.58 0 2 888

Number of killers claimed 0.23 0.43 0 2 888

Number of killers in closed balls 0.53 0.60 0 2 888

Player lied at least about one ball 0.53 0.50 0 1 888

Player lied at least about one value 0.32 0.47 0 1 888

Player lied at least about one killer 0.28 0.45 0 1 888

Number of killers taken to round 2 2.59 0.76 1 4 888

Round 2

Value of open balls (balls 5 and 6) 9651.32 14275.73 0 103000 666

Value claimed for balls 7, 8 and 9 18421.19 16683.73 105 95000 666

Value of closed balls (balls 7, 8 and 9) 13352.47 16291.90 0 95000 666

Number of killers in open balls 0.44 0.58 0 2 666

Number of killers claimed 0.44 0.52 0 2 666

Number of killers in closed balls 0.75 0.69 0 3 666

Player lied at least about one ball 0.45 0.50 0 1 666

Player lied at least about one value 0.23 0.42 0 1 666

Player lied at least about one killer 0.28 0.45 0 1 666

Number of killers taken to ﬁnal round 2.14 0.91 0 5 666

Value of balls taken to ﬁnal round 23003.79 21134.80 150 143300 666

Note that we deﬁned a social job as a job in which people care for other people, e.g., doctors, nurses, child minders, social workers, teachers, police

oﬃcers, ﬁremen, soldiers.

Large cities are cities with more than 268,300 inhabitants (based on the Mid-2008 Population Estimates published by the Oﬃce for National Statistics).

We estimated by personal judgment whether a player is below or above 40.

Players secretly make this statement about the strategy they plan to play in the ﬁnal before the show starts. It was introduced in episode 19, series 1.

Killer balls are counted as zero for all value variables.

Table 9: Summary statistics ﬁnal round

Variable Mean SD Min Max N

Final round (1st phase)

Potential jackpot 51238.36 31261.51 5000 168100 444

Average cash ball 6932.27 12030.86 10 75000 1122

Number of killers 3.21 0.94 1 6 144

Number of killers to bin 1.74 0.92 0 4 144

Number of killers to win 1.47 0.88 0 4 144

Jackpot/Pot. jackpot 0.25 0.28 0.0001 1 444

Final round (2nd phase)

Jackpot 13343.03 19247.56 3 100150 444

Decision (1 = split) 0.55 0.50 0 1 444

Outcome (0 = steal/steal, 1 = steal/split, 2 = split/split) 1.09 .75 0 2 222

Money taken home 4916.96 12000.86 0 100150 444

Money taken home (steal / split) 15693.11 20087.90 3 100150 94

Money taken home (split / split) 4783.64 8440.02 1.83 43950 148

Money left on the table 14426.34 20255.76 100 92330 108

Discussion (1 = starts discussion) 0.5 0.5 0 1 444

Handshake (1 = shake hands) 0.39 0.49 0 1 444

Mutual promise (1 = say promise) 0.25 0.43 0 1 444

Table 10: Cooperation rates by gender, series, demographics, and stake size

Split

Men Women All

(N=207) (N=237) (N=444)

Row % Row % Row % N

Exp erience

Unexperienced (Series 1) 44.4 59.1 52.5 80

Experienced (Series 2-4) 55.0 54.9 54.9 364

Age

≤ 40 44.3 53.1 49.2 260

> 40 64.1 59.8 62.0 184

Race

Non-White 46.2 42.9 44.4 27

White 53.6 56.5 55.2 417

England

Not from England 73.3 70.7 71.8 71

From England 49.4 52.3 50.9 371

Jackpot in £

[3, 500] 71.4 75.7 73.6 72

(500, 2500] 50.9 55.6 53.0 100

(2500, 10000] 56.0 50.0 52.9 102

(10000, 30000] 43.2 51.4 48.3 116

(30000, 100150] 43.5 51.6 48.1 54

Potential Jackpot in £

[5000, 30000] 46.3 51.7 49.1 114

(30000, 45000] 49.3 58.5 53.6 138

(45000, 75000] 52.3 58.3 55.8 104

(75000, 168100] 72.2 53.8 61.4 88

Exp ectation

Jackpot < Expectation 58.3 59.5 58.9 292

Jackpot ≥ Expectation 41.3 49.4 46.1 152

Total 53.1 55.7 54.5 444

Table 11: Mutual decision outcomes by series, demographics and stake size

(steal, steal) (steal, split) (split, split)

Row % Row % Row % N

Exp erience

Unexperienced (Series 1) 25.0 45.0 30.0 80

Experienced (Series 2-4) 24.2 41.8 34.1 364

Gender

Male Team 35.3 32.4 32.4 68

Female Team 16.3 55.1 28.6 98

Mixed Team 24.5 40.3 35.3 278

Age

Old Team (> 40) 11.8 50.0 38.2 68

Young Team (≤ 40) 23.6 48.6 27.8 144

Mixed Team 28.4 36.2 35.3 232

England

Not English Team 25.0 25.0 50.0 8

English Team 28.6 39.0 32.5 308

Mixed Team 14.3 52.4 33.3 126

Jackpot

≤ £500 8.3 36.1 55.6 72

> £500 27.4 43.5 29.0 372

Exp ectation

Jackpot < Expectation 23.3 35.6 41.1 292

Jackpot ≥ Expectation 26.3 55.3 18.4 152

Total 24.3 42.3 33.3 444

Winnings on Av. (0, 0) (15693, 0) (4784, 4784) 444

Table 12: Results from binary probit on unilateral cooperation (2)

y = 1 (Split) Marginal Eﬀects

Model (1) Model (2)

Player Characteristics

Unexperienced 0.031 (0.083) 0.011 (0.082)

Male -0.027 (0.066) -0.025 (0.065)

Age > 40 0.204*** (0.069) 0.203*** (0.069)

White -0.066 (0.149) -0.059 (0.148)

England -0.281*** (0.085) -0.277*** (0.086)

London -0.122 (0.116) -0.112 (0.114)

Large City 0.016 (0.087) 0.015 (0.086)

Student 0.009 (0.104) 0.034 (0.103)

Pensioner -0.216 (0.171) -0.234 (0.170)

Social Job (Reputation) -0.019 (0.097) -0.024 (0.096)

Team Characteristics

Index (Social Closeness) 0.509 (0.319) 0.529* (0.312)

Team Male -0.169* (0.101) -0.175* (0.099)

Team Female -0.083 (0.104) -0.076 (0.104)

Team Age> 40 -0.024 (0.111) -0.020 (0.111)

Team Age< 40 -0.049 (0.101) -0.055 (0.098)

Team White -0.036 (0.139) -0.033 (0.137)

Team England -0.049 (0.099) -0.013 (0.099)

Team Large City -0.185* (0.102) -0.179* (0.102)

Team Small City -0.116 (0.075) -0.094 (0.075)

Opponent Characteristics

Opp. Student 0.143 (0.105) 0.159 (0.103)

Opp. Pensioner 0.144 (0.193) 0.119 (0.190)

Opp. Social Job 0.026 (0.097) 0.020 (0.096)

Stake Size

log(Jackpot) -0.055*** (0.016)

log(Pot. Jackpot) 0.107* (0.056)

Jackpot < Expectation 0.164*** (0.063)

Communication

Started Discussion -0.024 (0.054) -0.022 (0.053)

Handshakes -0.150** (0.075) -0.183** (0.073)

Promise -0.050 (0.110) -0.080 (0.109)

Handshakes*Promise

0.326 ** (0.148) 0.367*** (0.058)

Player Characteristics

Voted against Opponent -0.295** (0.134) -0.301** (0.127)

Acc. Most Money in Round 1/2 -0.120* (0.062) -0.123** (0.061)

Selected Higher Values in Bin/Win -0.137 (0.087) -0.157* (0.085)

Binned Most Killers in Bin/Win -0.066 (0.103) -0.064 (0.102)

Lied About Cash Value -0.084 (0.064) -0.088 (0.064)

Lied About Killer -0.046 (0.061) -0.058 (0.059)

Opp. Lied About Cash Value 0.055 (0.065) 0.050 (0.065)

Opp. Lied About Killer -0.061 (0.061) -0.067 (0.060)

“Should Have Left The Game” 0.178*** (0.068) 0.183*** (0.065)

Wald X

80.52*** 76.05***

Log-Likelihood -226.45 -229.17

Pseudo R

0.15 0.14

N 386 386

Number of clusters 195 195

standard errors in parentheses are corrected for episode clusters; * p < 0.10, ** p < 0.05, *** p < 0.01

The marginal for the k-th independent variable is computed as

∂P (y=1|x

,D,G)

∂x

= φ(m)β

, k = 2, ..., K.

The marginal eﬀect of the interacted dummy variables “handshakes” (x

) and “promise”

) is computed as the discrete double diﬀerence:

P (y=1|x

,D,G)

= Φ(m)−Φ(β

+α+Dθ+Gν)−Φ(β

+α+Dθ+Gν)+Φ(α+Dθ+Gν).

Table 13: Results from ordered probit on outcomes in the PD (2)

y = 0; 1; 2 Marginal Eﬀects

Steal/Steal (0) Split/Steal (1) Split/Split (2)

Player Characteristics

Team Unexperienced 0.015 (0.066) 0.003 (0.010) -0.018 (0.075)

Team Male 0.094 (0.088) 0.005 (0.011) -0.099 (0.082)

Team Female 0.020 (0.064) 0.003 (0.010) -0.023 (0.074)

Team > 40 -0.065 (0.067) -0.021 (0.030) 0.086 (0.097)

Team < 40 0.104 (0.065) 0.012 (0.011) -0.116 (0.069)

Team England 0.109** (0.051) 0.034 (0.023) -0.143** (0.070)

Team Small City 0.069 (0.049) 0.013 (0.012) -0.082 (0.058)

Index -0.332** (0.165) -0.065 (0.047) 0.397** (0.197)

Pre-Play

Team Never Lied -0.055 (0.059) -0.016 (0.023) 0.070 (0.081)

Team Lying 0.029 (0.052) 0.005 (0.009) -0.035 (0.061)

Communication

Handshakes 0.097 (0.097) 0.019 (0.015) -0.116 (0.110)

Promise -0.062 (0.101) 0.125*** (0.021) 0.075 (0.119)

Handshakes*Promise -0.327*** (0.109) 0.035 (0.085) 0.361*** (0.134)

Stake Size

Jackpot < Expectation -0.161*** (0.055) -0.013 (0.015) 0.174*** (0.056)

Wald X

28.98**

Log-Likelihood -223.65

Pseudo R

0.06

N 54 94 74

Number of clusters 222

Standard errors in parentheses are corrected for episode clusters; * p < 0.10, ** p < 0.05, *** p < 0.01

Table 14: Voting decision by means of objective criteria

After round 1

After round 2

Criteria to predict a player in out in out

who should be voted to leave

Row % Row % Row % Row %

Cash-Criterion (CC)

ex-ante

stay 87.2 12.8 72.3 27.7

vote to leave 38.3 61.7 55.4 44.6

stated

stay 76.7 23.3 70.0 30.0

vote to leave 69.8 30.2 59.9 40.1

ex-post

stay 83.0 17.0 74.8 25.2

vote to leave 50.9 49.1 50.5 49.5

Killer-Criterion (KC)

ex-ante

stay 92.0 8.0 83.6 16.4

vote to leave 23.9 76.1 32.9 67.1

stated

stay 93.7 6.3 85.1 14.9

vote to leave 18.9 81.1 29.7 70.3

ex-post

stay 86.6 13.4 80.9 19.1

vote to leave 40.1 59.9 38.3 61.7

Cash-Killer-Criterion (CKC)

ex-ante

stay 87.7 12.3 73.2 26.8

vote to leave 36.9 63.1 53.6 46.4

stated

stay 83.3 16.7 74.1 25.9

vote to leave 50.0 50.0 51.8 48.2

ex-post

stay 83.2 16.8 74.5 25.5

vote to leave 50.5 49.5 50.9 49.1

N 666 222 444 222

We take into account that the prediction might not be unique per episode,

i.e., more than one player might have a prediction to be eliminated.

Each round, 222 contestants are eliminated. In round 1 (2) 55.4% (52.2%)

of the eliminated players are men.

Table 15: Voting decision per player by means of objective criteria

Players voted by means of

all (%) men (%) women (%)

Cash-Criterion (CC)

ex-ante

Round 1 72.4 74.5 70.5

Round 2 66.5 67.3 65.8

stated

Round 1 36.0 38.5 33.6

Round 2 64.4 62.6 66.1

ex-post

Round 1 55.3 55.4 55.3

Round 2 70.2 66.9 73.2

Killer-Criterion (KC)

ex-ante

Round 1 82.1 83.0 81.3

Round 2 81.9 84.9 79.1

stated

Round 1 83.6 85.5 81.8

Round 2 78.9 80.2 77.6

ex-post

Round 1 70.9 72.7 69.2

Round 2 76.3 77.0 75.6

Cash-Killer-Criterion (CKC)

ex-ante

Round 1 71.0 74.1 68.1

Round 2 65.8 67.3 64.4

stated

Round 1 55.0 58.3 51.9

Round 2 63.5 61.9 65.1

ex-post

Round 1 60.4 61.5 59.3

Round 2 66.8 65.5 68.1

573 278 (48.5%) 295 (51.5%)

Note: For purpose of comparability, we restrain the sample to 573 observa-

tions including only those players, who are not being eliminated in round

1. Further we consider only those decisions for which we can trace back

for whom a player voted, i.e., we exclude episodes with a voting of 2:1:1:0

in round 1 and 1:1:1 in round 2.

Table 16: Voting decision per player under risk or ambiguity (by means of objective criteria)

Round 2 Round 1

Players vote by means of Uncertainty Partial Ambiguity Ambiguity Ambiguity

(%) (%) (%) (%)

Cash-Criterion (CC)

ex-ante

all 64.0 66.3 67.2 72.4

men 82.4 64.9 67.7 74.5

women 54.5 67.6 66.7 70.5

stated

all 58.0 67.7 61.8 36.0

men 52.9 65.7 60.6 38.5

women 60.6 69.6 63.2 33.6

ex-post

all 74.0 70.2 69.3 55.3

men 70.6 66.4 66.9 55.4

women 75.8 73.6 71.9 55.3

Killer-Criterion (KC)

ex-ante

all 84.3 79.8 84.0 82.1

men 82.4 81.3 89.1 83.0

women 85.3 78.4 78.3 81.3

stated

all 84.0 75.9 81.3 83.6

men 94.1 76.9 81.9 85.5

women 78.8 75.0 80.7 81.8

ex-post

all 78.0 75.2 77.2 70.9

men 88.2 76.9 75.6 72.7

women 72.7 73.6 78.9 69.2

Cash-Killer-Criterion (CKC)

ex-ante

all 60.0 64.9 68.0 71.0

men 76.5 62.7 70.9 74.1

women 51.5 66.9 64.9 68.1

stated

all 70.0 61.7 64.3 55.0

men 70.6 59.0 63.8 58.3

women 69.7 64.2 64.9 51.9

ex-post

all 76.0 66.3 65.6 60.4

men 88.2 64.9 63.0 61.5

women 69.7 67.6 68.4 59.3

50 282 241 573

Note: The sample is restricted to the same 573 players in round 1 and 2.

Table 17: Ordered probit regression results on the number of votes (round 1)

= 0; 1; 2; 3 (Number of votes a player receives in round 1 per episode)

Marginal Eﬀects

No. of Votes Variables Model (1) Model (2)

0 Player Characteristics

Male -0.051 (0.035) -0.051 (0.035)

Age > 40 0.012 (0.034) 0.015 (0.034)

White 0.135** (0.058) 0.126** (0.059)

England -0.009 (0.045) -0.002 (0.046)

Order of Statements 0.021 (0.042) 0.016 (0.042)

Cash-Criterion (CC)

log(Value Open Balls) 0.097*** (0.010)

log(Value Stated Balls) -0.025 (0.019)

Truthful Statements 0.111*** (0.036)

Killer-Criterion (KC)

No. Killers Open Balls -0.159*** (0.040)

No. Killers Stated Balls -0.007 (0.050)

Truthful Statements 0.148*** (0.037)

Cash-Killer-Criterion (CKC)

log(Wght. Value Open Balls) 0.110*** (0.007)

log(Wght. Value Stated Balls) -0.011 (0.012)

Truthful Statements 0.138*** (0.036)

1 Player Characteristics

Male 0.007 (0.005) 0.008 (0.006)

Age > 40 -0.002 (0.005) -0.002 (0.005)

White -0.005 (0.005) -0.008** (0.004)

England 0.001 (0.006) 0.000 (0.007)

Order of Statements -0.003 (0.006) -0.003 (0.007)

Cash-Criterion (CC)

log(Value Open Balls) -0.013*** (0.002)

logsumvalueclaims1 0.003 (0.003)

Truthful Statements -0.011*** (0.004)

Killer-Criterion (KC)

No. Killers Open Balls 0.021*** (0.007)

No. Killers Stated Balls 0.001 (0.007)

Truthful Statements -0.012*** (0.003)

Cash-Killer-Criterion (CKC)

log(Wght. Value Open Balls) -0.017*** (0.003)

log(Wght. Value Stated Balls) 0.002 (0.002)

Truthful Statements -0.022*** (0.007)

2 Player Characteristics

Male 0.025 (0.017) 0.024 (0.017)

Age > 40 -0.006 (0.016) -0.007 (0.016)

White -0.064** (0.027) -0.060** (0.028)

England 0.004 (0.022) 0.001 (0.022)

Order of Statements -0.010 (0.020) -0.008 (0.020)

Cash-Criterion (CC)

log(Value Open Balls) -0.047*** (0.006)

logsumvalueclaims1 0.012 (0.009)

Truthful Statements -0.053*** (0.018)

Killer-Criterion (KC)

No. Killers Open Balls 0.076*** (0.020)

No. Killers Stated Balls 0.003 (0.024)

Truthful Statements -0.071*** (0.019)

Cash-Killer-Criterion (CKC)

log(Wght. Value Open Balls) -0.052*** (0.005)

log(Wght. Value Stated Balls) 0.005 (0.006)

Truthful Statements -0.066*** (0.018)

3 Player Characteristics

Male 0.020 (0.014) 0.019 (0.013)

Age > 40 -0.005 (0.013) -0.005 (0.013)

White -0.066* (0.036) -0.058* (0.034)

England 0.003 (0.017) 0.001 (0.017)

Order of Statements -0.008 (0.016) -0.006 (0.015)

Cash-Criterion (CC)

log(Value Open Balls) -0.037*** (0.005)

logsumvalueclaims1 0.010 (0.007)

Truthful Statements -0.046*** (0.016)

Killer-Criterion (KC)

No. Killers Open Balls 0.061*** (0.016)

No. Killers Stated Balls 0.003 (0.019)

Truthful Statements -0.066*** (0.019)

Cash-Killer-Criterion (CKC)

log(Wght. Value Open Balls) -0.041*** (0.004)

log(Wght. Value Stated Balls) 0.004 (0.004)

Truthful Statements -0.051*** (0.013)

Wald X

284.59*** 390.05***

Log-Likelihood -875.00 -870.64

Pseudo R

0.18 0.19

N 842 842

Number of clusters 211 211

standard errors in parentheses are corrected for episode clusters; * p < 0.10, ** p < 0.05, *** p < 0.01

Note: 11 special episodes are excluded (all players have the same sex)

marginal eﬀects:

∂P (y=j|X,P )

∂x

= [φ(ξ

j−1

− X β − P γ) − φ(ξ

− X β − P γ)]β

Table 18: Ordered probit regression results on the number of votes (round 2)

= 0; 1; 2 (Number of votes a player receives in round 1 per episode)

Marginal Eﬀects

No. of Votes Variables Model (1) Model (2)

0 Player Characteristics

Male -0.002 (0.037) -0.002 (0.037)

Age > 40 -0.030 (0.035) -0.033 (0.035)

White 0.039 (0.074) 0.031 (0.076)

England -0.045 (0.041) -0.047 (0.042)

Order of Statements 0.175*** (0.046) 0.170*** (0.045)

Lied in Round 1 -0.065** (0.031) -0.062** (0.031)

Cash-Criterion (CC)

log(Value Open Balls) 0.036*** (0.009)

log(Value Stated Balls) 0.005 (0.015)

Truthful Statements 0.177*** (0.047)

Killer-Criterion (KC)

No. Killers Open Balls -0.047 (0.040)

No. Killers Stated Balls -0.044 (0.033)

Truthful Statements 0.014 (0.054)

Cash-Killer-Criterion (CKC)

log(Wght. Value Open Balls) 0.040*** (0.007)

log(Wght. Value Stated Balls) 0.017* (0.010)

Truthful Statements 0.182*** (0.034)

1 Player Characteristics

Male 0.000 (0.000) 0.000 (0.000)

Age > 40 -0.000 (0.001) -0.000 (0.001)

White 0.002 (0.008) 0.001 (0.006)

England 0.002 (0.004) 0.002 (0.004)

Order of Statements -0.014* (0.007) -0.013* (0.007)

Lied in Round 1 -0.000 (0.001) -0.000 (0.001)

Cash-Criterion (CC)

log(Value Open Balls) -0.000 (0.001)

log(Value Stated Balls) -0.000 (0.000)

Truthful Statements 0.004 (0.003)

Killer-Criterion (KC)

No. Killers Open Balls 0.000 (0.001)

No. Killers Stated Balls 0.000 (0.001)

Truthful Statements 0.000 (0.001)

Cash-Killer-Criterion (CKC)

log(Wght. Value Open Balls) -0.000 (0.001)

log(Wght. Value Stated Balls) -0.000 (0.000)

Truthful Statements 0.004 (0.003)

2 Player Characteristics

Male 0.002 (0.037) 0.002 (0.037)

Age > 40 0.030 (0.036) 0.034 (0.036)

White -0.041 (0.082) -0.032 (0.082)

England 0.043 (0.037) 0.044 (0.038)

Order of Statements -0.161*** (0.039) -0.157*** (0.039)

Lied in Round 1 0.066** (0.031) 0.062** (0.031)

Cash-Criterion (CC)

log(Value Open Balls) -0.036*** (0.010)

log(Value Stated Balls) -0.005 (0.015)

Truthful Statements -0.181*** (0.049)

Killer-Criterion (KC)

No. Killers Open Balls 0.047 (0.040)

No. Killers Stated Balls 0.044 (0.033)

Truthful Statements -0.014 (0.055)

Cash-Killer-Criterion (CKC)

log(Wght. Value Open Balls) -0.040*** (0.007)

log(Wght. Value Stated Balls) -0.017* (0.010)

Truthful Statements -0.186*** (0.036)

Wald X

102.47*** 110.81***

Log-Likelihood -634.79 -633.74

Pseudo R

0.08 0.09

N 631 631

Number of clusters 211 211

standard errors in parentheses are corrected for episode clusters; * p < 0.10, ** p < 0.05, *** p < 0.01

Note: 11 special episodes are excluded (all players have the same sex)

marginal eﬀects:

∂P (y=j|X,P )

∂x

= [φ(ξ

j−1

− X β − P γ) − φ(ξ

− X β − P γ)]β

Working Papers of the Socioeconomic Institute at the University of Zurich

The Working Papers of the Socioeconomic Institute can be downloaded from http://www.soi.uzh.ch/research/wp_en.html

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