Prisoners and their dilemma

Journal of Economic Behavior & Organization 92 (2013) 163–175

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Prisoners and their dilemma夽 Menusch Khadjavi, Andreas Lange ∗ Department of Economics, University of Hamburg, Von Melle Park 5, 20146 Hamburg, Germany

a r t i c l e

i n f o

Article history: Received 24 January 2013 Received in revised form 3 May 2013 Accepted 30 May 2013 Available online xxx JEL classification: C72 C91 C93 K00

a b s t r a c t We report insights into the behavior of prisoners in dilemma situations that so famously carry their name. We compare female inmates and students in a simultaneous and a sequential Prisoner’s Dilemma. In the simultaneous Prisoner’s Dilemma, the cooperation rate among inmates exceeds the rate of cooperating students. Relative to the simultaneous dilemma, cooperation among first-movers in the sequential Prisoner’s Dilemma increases for students, but not for inmates. Students and inmates behave identically as second movers. Hence, we find a similar and significant fraction of inmates and students to hold social preferences. © 2013 Elsevier B.V. All rights reserved.

Keywords: Prisoner’s Dilemma Inmates Lab experiment Lab-in-the-field experiment

1. Introduction In 1950 Merrill M. Flood and Melvin Dresher conducted the first experiment of what they referred to as A Non-cooperative Pair (Flood, 1952, p. 17). Soon after this game was coined Prisoner’s Dilemma by Albert W. Tucker based on the illustrious story of two suspects who are taken into custody and questioned separately (Luce and Raiffa, 1957; Roth, 1993). In this classic story of Albert W. Tucker cooperation means to keep quiet about the crime, while defection means to testify against the other suspect. Ever since virtually countless research articles and books have dealt with the Prisoner’s Dilemma (e.g. Cooper et al., 1996; Ortmann and Tichy, 1999; Brandts and Charness, 2000; Clark and Sefton, 2001). It is one of the best known and most prominent examples used in almost all introductory game theory classes. It is surprising, however, that in 60 years of research on the Prisoner’s Dilemma and its applications,1 to the best of our knowledge no study was published that reports the behavior of prisoners themselves in dilemma situations that

夽 We are grateful to the JVA für Frauen in Vechta and especially Petra Huckemeyer and Elsbeth Lübbe for their dedicated cooperation and to the Kriminologischer Dienst in Lower Saxony for its permission to conduct this study. Sarah Mörtenhuber and Jan Papmeier provided excellent research assistance. ∗ Corresponding author. Tel.: +49 40428384035; fax: +49 40428383243. E-mail addresses: [email protected] (M. Khadjavi), [email protected] (A. Lange). Applications range from the arms race or oligopolistic competition for the two-player game, to voluntary public good provision reflected in an n-player Prisoner’s Dilemma (e.g., Axelrod, 1984). Besides studying one-shot dilemma situations, repeated interaction has received much interest. For example, Axelrod (1984) compares the performance of different strategies in an iterated Prisoner’s Dilemma with Anatol Rapoport’s simple Tit-for-Tat strategy proving to be especially robust against defection, yet able to achieve cooperation if encountering other cooperative programs. 1

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so famously carry their name. In this paper, we close this gap in the literature: we analyze the outcome of the original Prisoner’s Dilemma story, i.e. we study how actual prisoners behave in a simultaneous and a sequential Prisoner’s Dilemma. We compare their behavior to that of a conventional subject pool of university students in identical choice situations. From a methodological point of view, our study combines a conventional laboratory experiment with an artefactual field experiment (Harrison and List, 2004), i.e. a lab-in-the-field experiment with a different subject pool. Such investigation of the robustness of findings from conventional laboratory experiments with students has recently received increasing interest (Levitt and List, 2007). Some studies do not find significant differences between students and subjects recruited from more general pools (e.g. Anderson et al., 2013; Cleave et al., 2010; Stoop, 2012). Other studies focus on specific groups to capture behavioral differences (e.g., financial market professionals in Alevy et al., 2007, real estate brokers and nurses in Jacobson et al., 2011). Our study meanwhile analyzes another special part of society: inmates. Besides methodological reasons, we regard our study as useful in order to provide insights for behavioral law and economics. Jolls et al. (1998) and Korobkin and Ulen (2000) emphasize the importance of behavioral economic research on bounded rationality, bounded willpower and bounded self-interest for law and economics theory and policy. In this study we focus on bounded self-interest, i.e. the case when individuals hold other-regarding, social preferences. Meier (2007) discusses many settings in which these social preferences have been proven to play an important role for individual decision making. Rightfully convicted inmates are criminals who are addressed by specific policies such as conduct of the police force and courts, but also by prevention and reintegration programs. Hence, it is informative to examine how inmates react to incentives and whether they are similarly altruistic and cooperative when compared to a conventional subject pool. Naturally, a prison population differs along several dimensions from a students’ subject pool. For instance, in prison specific social norms may exist and post-experiment interaction may be more frequent. We nevertheless regard it as insightful to study decisions of real prisoners in comparison to students, while we may not conclusively identify the source of differences.2 Institutionalized populations have been used for early experimental economic studies on token economies (e.g., Ayllon and Azrin, 1965; Phillips, 1968; Battalio et al., 1974) as such institutions appeared to provide particularly controlled environments for economic experimentation (see Kagel, 1972). Several recent studies also investigate the behavior of inmates: Farrington and Welsh (2005) and Petrosino et al. (2006) summarize a number of criminological experiments: often these experiments can be regarded as case study evaluations of specific prevention or correction programs. Few studies take experimental economic methods to this field. Notable exceptions are Chmura et al. (2010) who analyze dictator game giving of 68 male inmates from a South German prison and find no significant difference of behavior compared to a sample of non-prison subjects’ results from a meta-study. Given that the dictator game is a good measure for altruistic behavior, they conclude that the prisoners in their study are not inherently more selfish than other subject pools. Birkeland et al. (2011) conduct experiments in Norway. They confirm dictator game findings of Chmura et al. and add evidence that this similarity does not depend on whether the game is played between prisoners, subjects from the general public or an interaction of the two groups. Hence, the two studies provide evidence that (male) prison subjects, students and subjects drawn from the general public are comparably altruistic in the dictator game. In our experiment, we study social preferences beyond such altruism: Based on a simultaneous and a sequential version of a Prisoner’s Dilemma game, we measure conditional and unconditional cooperativeness of inmates and students and provide a nuanced picture to the literature:3 We find that in the simultaneous Prisoner’s Dilemma only 37% of students choose to cooperate, relative to an individual cooperation rate of 56% among inmates. Inmates are therefore able to better solve their classical dilemma situation than students: on average one can expect inmates to mutually cooperate in 30% of cases, while only 13% of students’ pairs fully cooperate. In contrast, we find an equal share of about 60% of students and inmates to return cooperation in response to a cooperating first-mover in the sequential Prisoner’s Dilemma. In both subject pools defection by the first mover will be answered with defection. We thereby obtain results on conditional cooperation consistent with Chmura et al. (2010) and Birkeland et al. (2011) results for dictator game giving. In this sequential Prisoner’s Dilemma, 63% of first movers among students choose to cooperate, thereby significantly more than in the simultaneous choice situation. Conversely, among prisoners, the individual cooperation decision of first movers does not significantly differ from the individual cooperation decision in the simultaneous game. As such, collective cooperation rates, i.e. the percentage of cases in which both players cooperate, are significantly larger in the sequential than in the simultaneous game for students (39% vs. 13%), while no such difference is observed for inmates (27% vs. 30%). The remainder of this paper is organized as follows: we discuss predictions and outline the experimental design and procedures in prison and at university in Section 2. We present and discuss the results of our study in Section 3, before drawing conclusions in Section 4.

2 It would also be interesting to see if behavioral differences can be explained by the severity of the committed crime and to compare the behavior of female and male inmates. 3 Note that differences may, for example, be driven by gender effects or by the different (and probably less severe) nature of committed crimes.

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Table 1 The Prisoner’s Dilemma. Player 2

Player 1

Cooperate Defect

Cooperate

Defect

7, 7 9, 1

1, 9 3, 3

2. Experimental design and predictions We employ a 2 × 2 experimental design to analyze simultaneous and sequential Prisoner’s Dilemma decision making within and between the two groups of our study, i.e. female university students and female inmates.4 Payoffs for the Prisoner’s Dilemma are depicted in Table 1. 2.1. Theory and predictions In the simultaneous Prisoner’s Dilemma, two players decide simultaneously to either cooperate with the other player or to defect. Assuming standard homo economicus characteristics for both players, defection is the dominant strategy such that the unique Nash equilibrium is given by mutual defection, with payoffs of 3 to both players in our formulation. Conversely, mutual cooperation would generate payoffs of 7 to both players and thereby Pareto dominates the Nash equilibrium. For the sequential Prisoner’s Dilemma, backward induction clearly generates identical result: complete defection forms the unique subgame-perfect Nash equilibrium. Differently from these predictions, considerable cooperation rates are found in experimental studies as early as Flood (1952) to recent studies like Cooper et al. (1996) and Clark and Sefton (2001). A number of theories can help to explain the motivation of individuals, most prominently theories of social preferences that, for example, incorporate comparisons of an individual’s own payoff with payoff of other players (Fehr and Schmidt, 1999; Bolton and Ockenfel, 2000) or directly include motives of reciprocity (Dufwenberg and Kirchsteiger, 2004; Falk and Fischbacher, 2006). We derive the equilibrium using the example of Fehr and Schmidt (1999) preferences in the Appendix. However, the qualitative insights hold for a large class of social preferences and are discussed in the following.5 In the simultaneous Prisoner’s Dilemma, an individual with such social preferences may choose to cooperate if she believes that a sufficiently large proportion of other players also cooperate. That is, without social preferences or with a belief that others very likely defect, she will ‘respond’ with defection in order to avoid the sucker payoff. In the sequential Prisoner’s Dilemma, backward induction trivially shows that a second player with sufficiently strong social preferences would choose to cooperate in response to a cooperating first-mover. Conversely, both purely selfinterested as well as individuals with social preferences would generally defect in response to first player’s defection. This leads to the following prediction: Prediction 1. The share of cooperative second-mover decisions in response to first-mover cooperation is expected to be larger than the share of cooperative players in the simultaneous Prisoner’s Dilemma, while cooperation in response to defection of the first mover is expected to be almost non-existent. The first mover choice therefore importantly depends on her beliefs on the preferences of the second mover. If the first mover assumes that the second mover holds social preferences and will decide to cooperate given first-mover cooperation (and defect given first-mover defection), the first mover may decide to cooperate even without holding social preferences herself. Prediction 2. The share of cooperative first movers in the sequential Prisoner’s Dilemma is expected to be at least as large as the share of cooperative players in the simultaneous Prisoner’s Dilemma. In our experiment, our prime interest was to observe the rates of cooperation among prisoners in their famous dilemma situation, both in sequential as well as in the simultaneous formulation. As most previous experiments used students subject pools, we additionally compare the behavior of prisoners with those of students in equivalent tasks. We both report findings for individual cooperation decisions as well as the extent of collective cooperation, i.e. pairs where both players cooperate.

4 The Prisoner’s Dilemma decisions discussed in this paper are part of a sequence of games we analyze in a series of companion papers. All decisions were made one-shot without feedback, except for the second mover in the sequential Prisoner’s Dilemma: here subjects received information about the choice of the first mover. The sequence of games was the following: (1) a stealing game with deterrence incentives (see Khadjavi, 2013), (2) either a simultaneous or sequential Prisoner’s Dilemma (discussed in this paper), (3) a lottery, (4) a dictator game, and (5) a task to measure individual discount rates. We find no correlation between decision making in the first game and the Prisoner’s Dilemma. Thus we cannot reject the null hypothesis that decision making in the Prisoner’s Dilemma was independent from the first game and are able to safely analyze our data. 5 Note again that – in line with these theories – potential differences between the prisoners and students could relate to a different composition of social preferences. However, the causes of these differences may stem from social norms being established in the prison environment, different levels of social distance, or different age structures such that we cannot fully identify the causality of the differences.

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2.2. Experimental setup The five sessions with prisoners were conducted at JVA für Frauen (penitentiary for women) in Vechta, Germany, on June, 14 2012.6 It is the central women’s prison in the German state of Lower Saxony (in North-Western Germany, bordering the City of Hamburg) with a capacity for about 150 detained women in its main section. Inmates serve sentences between a couple of days and life sentence, with an average detention time period of 6 months. It offers facilities for mother-and-child care and social therapy as well as secondary school education and apprenticeship opportunities such as cooking and painting. Women are additionally able to earn money for their release savings and phone accounts by sewing for a company that produces bags within the prison grounds. About 50% of women are convicted for drug-related crimes.7 Three weeks before the experiment we distributed invitations for participation in the study. The invitation included information on the nature of the experiment, that participation is strictly voluntary, and that we guarantee absolute anonymity. In German prisons it is not possible to earn cash, so that we needed to apply an alternative payment vehicle. The state institution which was responsible for permitting our study suggested using coffee, tobacco and phone credit as alternatives. Consequently participants were able to earn either a jar of instant coffee (200 g) or a pack of tobacco (40 g) as show-up fees. The monetary value of both show-up fee options was close to 5 EUR. We ordered coffee and tobacco from the prison’s delivery company and both the brand of coffee and of the tobacco were most commonly used in the prison. Participants were also informed that they will receive individual phone credit depending on their decisions in the study. This way we were able to create a quasi-continuous payoff space for the experiment decisions. The day before the experiment we set up a mobile computer lab with 20 terminals, i.e. laptops and separation walls, in the prison’s gymnasium. Three sessions took place in the morning and two sessions were conducted in the afternoon. The four sessions with student subjects were conducted in the experimental economic laboratory of the School of Economics, Business, and Social Sciences at the University of Hamburg about three weeks later, in the first week of July, 2012. Female students were recruited via ORSEE (Greiner, 2004) from the subject pool which comprises students of different majors. In order to allow a better comparison with inmates, we also recruited a significant number of student subject who were relatively new to the subject pool and had therefore less (or no) experience with lab experiments. Similar to the inmates in the lab-in-the-field setting, student subjects received information that they can receive earnings by making anonymous decisions on computer terminals. The payment vehicle for student subjects was the usual: a sum of cash consisting of a 5-EUR show-up fee and money determined by decision made in the experiment. 90 female inmates participated in our lab-in-the-field sessions, while 92 female students participated in our conventional lab sessions, yielding a total of 182 subjects. We observe 46 students and 36 inmates in the simultaneous Prisoner’s Dilemma as well as 46 students and 54 inmates in the sequential Prisoner’s Dilemma. In the simultaneous treatment, each subject made one choice and upon completion of the experiment was randomly matched with one other subject to determine the payoffs. In the sequential treatment, each subject first made a first-mover decision and then was randomly matched with one other subject, received information about this other subject’s first mover choice and then decided as a second mover. After completion of the experiment, the roles that mattered for payment were randomly determined. Each subject participated in only one treatment. At the end of the experiment, we employed an ex-post survey to obtain important demographic variables, for instance education and marital status.8 We used Taler as the experimental currency, with 1 EUR equal to 5 Taler. Average earnings in the Prisoner’s Dilemma games were 4.48 Taler among students and 4.87 Taler among prisoners. Including the show-up fees, average earnings in prison were 14.40 EUR compared to 13.20 EUR in the students’ lab. Note that these earnings depend on decisions in all five games of the experiment. In total, experimental sessions lasted 45–60 minutes. We used z-Tree (Fischbacher, 2007) to program and run our experiment. 3. Results Our experimental design enables us to compare cooperation rates among prisoners and students and to test our predictions on their differences between simultaneous and sequential Prisoner’s Dilemma games. We concentrate on individual cooperation decisions, but also report the extent to which subject pairs overcome the dilemma, i.e. where both players choose to cooperate. Table 2 reports summary statistics of individual choices in the respective treatments as well as on demographic variables obtained in the ex post survey. Fig. 1 illustrates the experimental results graphically. In prison, 55.6% of inmates cooperated in the simultaneous Prisoner’s Dilemma. This compares to a cooperation rate of 37.0% among students. This difference is significant at the 10% level based on a Pearson’s 2 test (see Table 3a). This result suggests a relatively strong tendency to cooperate among prisoners, enabling them to often overcome the dilemma situation: Table 3b reports the collective cooperation rates, i.e. when both players of a randomly matched pair cooperate (13.1% for students vs. 30.2% for inmates, different at p < 0.000, Pearson’s 2 test).

6

Further information (in German) on the JVA für Frauen in Vechta: www.jva-fuer-frauen.niedersachsen.de. It would be worthwhile to investigate the relationship between the severity of the committed crime and cooperation decisions. Unfortunately, our data does not allow such an investigation. The tradeoff was to either keep the guarantee of anonymity or to ask exact questions about the committed crime but to effectively lift anonymity. We consciously opted for strict anonymity. 8 Ex-post demographic questionnaire answers are missing for 18 prisoners due to IT problems at the end of one session. 7

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Table 2 Summary statistics. Variable

Students

Prisonersa

N

92 46 46

90 36 54

36.97 (17/46) 13.14

55.56 (20/36) 30.16

63.04 (29/46) 62.07 (18/29) 0.00 (0/17) 39.08 23.35 6 (All in top category) 8.33 6.52 4.35 19.56 60.87

46.30 (25/54) 60.00 (15/25) 3.45 (1/29) 27.32 31.43 1.47 None 16.67 59.72 90.28 84.72

In simultaneous PD In sequential PD Simultaneous PD: Individual cooperation rate (in %) Expected full cooperation rateb (in %) Sequential PD: First stage individual cooperation rate (in %) If the first mover cooperated: second stage cooperation rate (in %) If the first mover defected: second stage cooperation rate (in %) Expected Full Cooperation Rateb (in %) Mean age (in years) Mean educationc Mean experiment experience (in sessions) Rate of married subjects (in %) Rate of subjects with children (in %) Rate of smokers (in %) Rate of coffee drinkers (in %)

Note: We collected socio-demographic data on coffee and tobacco habits for another part of the larger prison study. Nevertheless it should not hinder our analysis to control for such habits, so that we report them here as well. a Ex-post demographic questionnaire answers are missing for 18 subjects in prison due to IT problems at the end of one session (‘fortunately’ only after the decision-making part of the experiment). b To calculate the full cooperation rate, we formed all possible pairs of two distinct players and considered the ratio of pairs for which both players cooperated. c The German education system is rather complicated and comparing education quantitatively is tedious. We transferred questionnaire data on education into qualitatively ascending categories which are roughly in accordance with years of schooling: no school diploma = 0; 9-year high school diploma = 1; 10-year high school diploma = 2; 13-year high school diploma = 3; completed apprenticeship = 4; completed master craftsman diploma = 5; academic education = 6.

Fig. 1. Cooperation rates of students and prisoners, simultaneous and sequential PD. Table 3a Testing differences between individual cooperation decisions. Group treatment

Students

Prisoners

Test statistic

Simultaneous PD Sequential PD Test statistic

36.97% 63.04% Pearson’s 2 : 6.261, p = 0.012

55.56% 46.30% Pearson’s 2 : 0.741, p = 0.389

Pearson’s 2 : 2.821, p = 0.093 Pearson’s 2 : 2.805, p = 0.094

Note: Test statistics refer to the respective row or column. For instance, comparing individual cooperation rates in the simultaneous Prisoner’s Dilemma among students and inmates (36.97% vs. 55.56%), Pearson’s 2 test (with one degree of freedom) yields a test statistic of 2.821 which corresponds to a p-value of 0.093 (i.e. there are significantly more inmate subjects choosing to cooperate than students). Table 3b Collective cooperation rates (both player cooperate). Group treatment

Students (%)

Prisoners (%)

Simultaneous PD Sequential PD

13.14 39.08

30.16 27.32

Note: To calculate the full cooperation rate, we formed all possible pairs of two distinct players and considered the ratio of pairs for which both players cooperated.

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Conversely, 63.0% of students as first movers in the sequential Prisoner’s Dilemma choose the cooperative strategy compared to 46.3% among inmates. These rates are again significantly different at the 10% level (see Table 3a). Our comparison of inmates with students therefore finds a striking disparity in both sequential and simultaneous Prisoner’s Dilemma games. Result 1. On average, prisoners behave more cooperatively than students in a simultaneous Prisoner’s Dilemma. Conversely, student first movers in the sequential Prisoner’s Dilemma are more likely to cooperate than inmates in this position. To further explore the drivers behind these behavioral differences, we take a closer look at the choices in the simultaneous game relative to those of first movers in the sequential Prisoner’s Dilemma. Here, we find no significant change for inmates (p = 0.389), while individual cooperation levels among students are significantly larger in the sequential than in the simultaneous game (Pearson’s 2 , p = 0.012).9 This behavioral impact of the sequentiality of choices is consistent with Prediction 2. Result 2. The share of cooperative first movers in the sequential Prisoner’s Dilemma is at least as large as the share of cooperative players in the simultaneous Prisoner’s Dilemma. It is greater among students, while no significant difference is found for inmates. While we have so far concentrated on comparisons between the behavior of students and inmates on average, it is obvious that these two groups differ with respect to important socio-demographic differences (see Table 2). We additionally examine our treatment effects based on a series of Probit estimations (reported in Table 4).10 The baseline estimations I and II confirm our treatment effects as stated in Results 1 and 2. When controlling for all of our socio-demographic variables in column III of Table 4, interestingly, all demographic control variables remain insignificant with one exception: we find that coffee drinkers are more cooperative than those who do not drink coffee. We refrain from speculating about the underlying reasons. The difference between individual cooperation rates among inmates and students turns insignificant (even though keeping the positive sign) which is possibly caused by the smaller number of observations.11 The other effects remain: while cooperation increases for first movers in the sequential Prisoner’s Dilemma compared to individual cooperation decisions of players in the simultaneous Prisoner’s Dilemma (‘SEQ’ is positive and significantly different from zero at the 5% level), this effect is offset by the interaction term ‘Prisoner × SEQ’. Theoretically, the differences between the choices of first-movers in the sequential game and choices in the simultaneous game as reported in Result 2 are driven by the anticipation of second mover choices as conditional cooperators. We now analyze those in detail. Second mover cooperation rates among students and inmates are strikingly similar: 62.1% of students and 60.00% of inmates returned cooperation of first movers (Pearson’s 2 : 0.0242, p = 0.876). Conversely, defection by the first player is answered with defection by all but one second mover. Hence, we find convincing evidence of conditional cooperation. Relative to the individual cooperation levels in the simultaneous Prisoner’s Dilemma, we can formulate the following result. Result 3. Students and inmates are equally reciprocating when facing cooperation from the first mover. Cooperation rates of second movers responding to a cooperating first mover are at least as high or greater than in the simultaneous Prisoner’s Dilemma. Result 3 is consistent with the theoretical Prediction 1. It also indicates that cooperativeness among inmates and students is similar when no strategic uncertainty regarding the choice of the other player exists. Our design allows us to further relate the decision of a second mover with the one she had taken as a first mover. A Probit regression reported in Table 4 (column IV) links the individual decision to cooperate as a second mover to three important features: whether she herself cooperated in the first-mover stage, whether she faces first-mover cooperation or defection, and whether the second mover is a student or an inmate. While confirming Result 3 and controlling for the first mover’s decision, we find that the probability for an individual to cooperate as a second mover is significantly larger if she decided to cooperate as a first mover herself. We confirm this finding by Pearson’s 2 tests for both inmates (p = 0.045) and students (p = 0.011). Combining the decisions of first and second movers, we find collective cooperation rates (both player in a pair cooperating) of 39.1% among students and 27.3% among inmates in the sequential Prisoner’s Dilemma (see Table 3b). Students therefore are significantly more likely to overcome the dilemma in the sequential than in the simultaneous setting. For inmates, no significant difference in collective cooperation rates exists between the simultaneous and the sequential Prisoner’s Dilemma.

9 This finding is in contrast to Brandts and Charness (2000) who find no difference in behavior of their student subjects. One possible explanation is that Brandts and Charness employ the strategy method for their second mover choices, while our participants only react to actual choices. Brandts and Charness (2011) discuss this issue themselves. Another explanation may be that we solely analyze female subjects while we assume that Brandts and Charness invited a mix of males and females. This second explanation is indeed supported by Ortmann and Tichy (1999) who find females to be more cooperative in the first period of their multi-period experiment. 10 As different as the numbers in the summary statistics may appear, we find enough heterogeneity in survey answers for both groups in order to include these variables in one regression model. 11 Due to the missing ex-post demographic questionnaire answers from one session in prison, this regression relies on 164 instead of 182 observations.

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Table 4 Probit regressions estimating drivers of individual cooperation decisions. Independent variable

Dependent variable: cooperation I SIM

II SIM & SEQ (1st stage)

III SIM & SEQ (1st stage)

IV SEQa (2nd stage)

Cooperation in 1st stage (Dummy)

0.818** (0.337)

1st mover cooperation (Dummy)

2.288*** (0.443) 0.473* (0.282)

0.221 (0.719)

SEQ (Dummy)

0.666** (0.267)

0.643** (0.278)

Prisoner × SEQ (Dummy)

−0.899** (0.380)

−1.018** (0.436)

Prisoner (Dummy)

0.473* (0.282)

Age (Continuous)

0.006 (0.016)

Education (Continuous)

−0.092 (0.112)

Married (Dummy)

0.312 (0.353)

Mother (Dummy)

−0.259 (0.303)

Coffee drinker (Dummy)

0.698** (0.271)

Smoker (Dummy)

−0.089 (0.342)

Experiment experience (Continuous)

−0.013 (0.017)

−0.049 (0.332)

Constant

−0.333* (0.189)

−0.333* (0.189)

−0.157 (0.668)

−2.445*** (0.483)

N

82

182

164

100

Note: Probit estimations, Student is the baseline in all estimations. Standard errors in parentheses, significance. * p < 0.10. ** p ≤ 0.05. *** p < 0.01. a We do not include socio-demographic variables in estimation IV as we run into overfitting issues. An analysis of pairwise correlations between cooperation as a second mover in the sequential Prisoner’s Dilemma and socio-demographic variables does not yield any significant dependencies.

4. Conclusion Despite being one of the most prominent examples of game theory, up to now the Prisoner’s Dilemma has not been studied with the population that motivated its naming. In this paper, we studied choices of female inmates in a simultaneous and sequential Prisoner’s Dilemma and compared those with a female student population. We find that more than half of the inmates choose to cooperate in the simultaneous Prisoner’s Dilemma, thereby (marginally) exceeding the ratio of cooperating students. While cooperation among students in the sequential Prisoner’s Dilemma is larger than in the simultaneous choice situation, no such increase can be observed among inmates. However, the rate of conditional cooperators is almost identical between the two subject pools. We thereby find nuanced differences between the behavior of inmates and the more standard pool of female students. In line with findings of Chmura et al. (2010) and Birkeland et al. (2011), the share of inmates vs. students that apparently hold social preferences as evidenced by second mover choices is almost identical. Such external validity with respect to our focus group is good news for experimental research. Additionally, it may – speculatively – provide evidence that criminal behavior does not appear to be a self-selection process by which purely self-interested individuals are more likely to commit crimes than socially oriented individuals. It is striking, however, that the cooperation rate among students is larger in the sequential game for first-movers than in the simultaneous game, while no such difference is observed for inmates. Theoretically, even self-interested individuals may

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choose to cooperate as first-movers if they expect a sufficiently large share of conditional cooperators.12 One explanation for the different impact of sequential choices on cooperation rates could be that narrowly self-interested students hold such pro-social beliefs about second movers, while similarly motivated inmates do not (or to a lesser extent) and instead appear as playing against same-minded self-interested individuals. The investigation of potential differences in the ability of anticipating others’ strategies could be a fruitful research avenue with far reaching implications for law and economic policy. Appendix A. Equilibria based on Fehr and Schmidt (1999) Preferences in Fehr and Schmidt (1999) explicitly model inequality aversion. Utility of player i when receiving payoff i with player j receiving j is given by ui = i − ˛i max {0, j − i } − ˇi max {0, i − j } where 1 > ˇi ≥ 0 is the weight given on advantageous inequality, while ˛i ≥ ˇi is the weight put on disadvantageous inequality. A.1. Simultaneous Prisoner’s Dilemma Assuming a probability  of the other player cooperating, the expected utility from player i choosing to cooperate is given by: E[ui , c] = 7 + (1 − ) (1 − ˛i (9 − 1)) while defecting gives the expected utility E[ui , d] = (9 − ˇi (9 − 1)) + (1 − )3 Therefore player i chooses to cooperate if E[ui , c] ≥ E[ui , d], i.e. if ˇi ≥

1 1− + (1 + ˛i ) 4 

(A.1)

which is equivalent to ˛i ≤

3 + 4ˇi  − 4 4(1 − )

(A.2)

That is, a player cooperates if his aversion towards advantageous inequality is sufficiently large or the aversion towards disadvantageous inequality is not too strong. If  converges to 1, the inequality holds if ˇi ≥ 1/4 such that all players cooperating could only be an equilibrium if all agents are sufficiently inequality averse with ˇi ≥ 1/4. Conversely, players with ˇi < 1/4 will never choose to cooperate, while the decision for those with ˇi ≥ 1/4 depends on their beliefs on the action of others, i.e. on the probability of being matched with a cooperating partner according to (A.1). A.2. Sequential Prisoner’s Dilemma Solving the game backwards, a player would choose to cooperate when being matched with a cooperating player 1 if: E[ui , c → c] = 7 ≥ 9 − ˇi (9 − 1) = E[ui , c → d] that is, if ˇi ≥

1 4

(A.3)

As a response to a defecting player 1, all agents are predicted to defect as cooperation would lead to less payoff and induce inequality. ˆ Then, player 1 would choose to cooperate if his expected utility Let us denote the fraction of players with ˇi ≥ 1/4 by . from cooperating is larger than from defecting: 7 ˆ + (1 − )(1 ˆ − ˛i (9 − 1)) ≥ 3 Or – equivalently – if ˛i ≤

ˆ −1 3 ˆ 4(1 − )

(A.4)

12 Note that 21 (11 students and 10 inmates) out of 100 subjects do not cooperate as second mover when matched with a cooperating first-mover, even though having cooperated in their first-mover choice themselves.

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Note, for example, that a selfish player 1 (˛i = 0) would choose to cooperate if she anticipates more than one third of players to be conditional cooperators. Inequality averse players would require even a larger  ˆ to cooperate. If, however,  ˆ < 1/3, no player would choose to cooperate. A.3. Comparison of simultaneous and sequential Prisoner’s Dilemma Comparing (A.1) and (A.3) directly shows that the fraction of conditional cooperators in the sequential PD game, i.e. those that cooperate if matched with a cooperating player 1, is at least as large as the fraction of cooperating players in the ˆ simultaneous PD game, i.e.  ≤ . Prediction 1. The share of cooperative second-mover decisions in response to first-mover cooperation is expected to be larger than the share of cooperative players in the simultaneous Prisoner’s Dilemma, while cooperation in response to defection of the first mover is expected to be almost non-existent. Further considering the right hand side of (A.2), we obtain that for all cooperating players in the simultaneous PD game:˛i ≤

3+4ˇi −4 4 (1−)

≤

3+4ˇ ˆ ˆ i −4 4 (1−) ˆ

≤

3−1 ˆ where 4 (1−) ˆ

we used ˇi ≥ 1/4 to obtain the last inequality. Using (A.4), the range of

˛-parameter for which a player in the simultaneous Prisoner’s Dilemma cooperates is smaller than the range for the player 1 in the sequential Prisoner’s Dilemma. We therefore obtain Prediction 2. The share of cooperative first movers in the sequential Prisoner’s Dilemma is expected to be at least as large as the share of cooperative players in the simultaneous Prisoner’s Dilemma.

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Appendix B. Experiment Instructions (translated from German into English)

General Instructions for Participants Welcome to the Study! Thank you for participating in our study today. You will be able to earn a considerable amount of money. It is therefore important that you read these instructions carefully. It is prohibited to communicate with other participants during the study. Should you have any questions please raise your hand and an instructor will come to answer them. If you violate this rule, we will have to exclude you from the study and from all payments. During the experiment you will make decisions anonymously, other participants will not learn about your decisions. In any case you will earn [Inmates: a pack of coffee or a pack of tobacco; Students: 5 Euros] for participation in this experiment. The additional earnings depend on your decisions[Inmates: and will be paid to your phone account]. During the study your earnings will be calculated in Taler. At the end of the experiment your earned Taler will be converted into Euros at the following exchange rate: 1 Taler = 0.20 €. The study consists of five independent tasks.Your decision in a task does not have any impact on the other tasks. The instructions for the five tasks will be handed out one after another. You will first receive instructions for task 1 and then make your decision at the computer terminal. After this task 1 is done. Thereafter you will receive instructions for task 2 and again make your decision at the computer terminal. This procedure continues until the end of the study. In the end we will also ask you to answer some general questions. At the end of the study you will receive your payment. Your payment is the sum of payments from all five tasks. All earned Taler will be converted to Euros an d paid to you [Inmates: in addition to a pack of coffee or tobacco]. Hence you will get Your total payment = Your payment from task1, 2, 3, 4 and 5 + [Inmates: a pack of coffee or tobacco, Lab: 5 EUR] All payments will be done separately, without any other participant being able to see what you have earned. Apart from the instructor nobody will know what you have earned.

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[We skip the instructions for task 1. Also we do not include instructions for tasks 3 to 5 in this appendix. They will be included in companion papers on our prison study and are available upon request. Readers interested in the original German instructions may also contact us.]

Instructions for Task 2

[Simultaneous Prisoner’s Dilemma:] In task 2 you can choose between two options: Option A and Option B. Another person, who is randomly matched with you, also chooses between Option A and Option B. Your payment and the payment of the other person depend on your own decision and the decision of the other person: If you choose Option A and the other person also chooses Option A, then you will receive 7 Taler and the other personwill also receive7 Taler. If you choose Option B and the other person chooses Option A, then you will receive 9 Taler and the other person will receive 1 Taler.

If you choose Option A and the other person chooses Option B, then you will receive 1 Taler and the other person will receive 9 Taler.

If you choose Option B and the other person also chooses Option B, then you will receive 3 Taler and the other person will also receive 3 Taler. Summarizing in an overview: Your choice A B A B

The choice of the other person A A B B

Your payment 7 9 1 3

The payment of the other person 7 1 9 3

You and the randomly matched other person choose at the same time. Please choose on the computer screen whether you decide for A or B.

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Instructions for Task 2

[Sequential Prisoner’s Dilemma:] In task 2 you can choose between two options: Option A and Option B. Another person, who is matched with you, also chooses between Option A and Option B. Your payment and the payment of the other person depend on your own decision and the decision of the other person: If you choose Option A and the other person also chooses Option A, then you will receive 7 Taler and the other personwill also receive 7 Taler. If you choose Option B and the other person chooses Option A, then you will receive 9 Taler and the other person will receive 1 Taler.

If you choose Option A and the other person chooses Option B, then you will receive 1 Taler and the other person will receive 9 Taler.

If you choose Option B and the other person also chooses Option B, then you will receive 3 Taler and the other person will also receive 3 Taler. Summarizing in an overview: Your choice A B A B

The choice of the other person A A B B

Your payment 7 9 1 3

The payment of the other person 7 1 9 3

The decision takes place one after another. This means that first person 1 chooses between Option A and Option B. This choice will then be sent to person 2 before she makes her decision between Option A and Option B.

All participants make their decisions between Option A and Option B as person 1. Your choice is then sent to a matched participant before she chooses between Option A and Option B as person 2. Conversely another participant will be matched with you. You will receive information on the choice of this person and then choose between Option A and Option B as person 2. At the end of the experiment half of the participants will be drawn as person 1 and the other half as person 2. Your choice as person 1 will count towards your payment if you are drawn as person 1. If you are drawn as person 2, then you will receive your payment based on the decision you have made as person 2.

Please first decide for Option A or Option B as person 1 at the computer screen. Afterwards you will see a second screen on which you make your decision as person 2. The screen will inform you about the choice of the matched person 1.

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