One-shot Prisoner's Dilemma Game Research Articles

Empirically testing a relationship between cooperation and the prime numbers.

Theoretical models suggest a relationship between cooperation and the prime numbers. In environments where agents play multiple one-shot prisoner's dilemma games per generation, cooperators evolve to fixation more frequently when cooperating on a cyclical schedule with a prime-number period length. This finding parrots classic predator-prey models showing selection for prime-number prey life cycles. Here, I report an empirical test of the former models using previously published data concerning humans playing one-shot public goods games across multiple time points-i.e. an analogue to multiple one-shot prisoner's dilemma games. I find very modest evidence of cyclicality at prime-numbered time intervals, though results indicate rough agreement between theoretical predictions and observed rates of full cooperation across time points. Analyses of individual decisions find increased contributions to the public good at prime-number time points and separate placebo tests indicate a 4-in-1000 chance of spuriously estimating this effect. However, when exploratory analyses exclude low-value prime-numbered time points, the magnitude of the estimated effect decreases and the hypothesis of no effect cannot be rejected, implying that low-value, prime-number time points drive estimates, contrary to theoretical model predictions. These findings cast doubt on the hypothesis of increased cooperation at prime-number time points-at least among humans playing public goods games.

The role of payoff parameters for cooperation in the one-shot Prisoner's Dilemma

The Prisoner's Dilemma is arguably the most important model of social dilemmas, but our knowledge about how its material payoff structure affects cooperation is incomplete. We investigate the effect of variation in material payoffs on cooperation in one-shot Prisoner's Dilemma games. We report results from three experiments (N = 1,993): in a preliminary experiment, we vary the payoffs over a large range. In our first main experiment (Study 1), we present a novel design that varies payoffs orthogonally in a within-subjects design. Our second main experiment, Study 2, investigates the orthogonal variation of payoffs in a between-subjects design. In a complementary analysis we also study the closely related payoff indices of normalized loss and gain, and the K-index. A robust finding of our experiments is that cooperation increases with the gains of mutual cooperation over mutual defection.

Prime numbers and the evolution of cooperation, II: Advantages to cooperators using prime-number period lengths in a finite population constrained to prisoner's dilemma strategies that alternate between periods of activity and inactivity

• The paper reports a model of a finite population of agents constrained to strategies that alternate between activity and inactivity (a.k.a. temporal partitioning) in a social environment where multiple one-shot prisoner's dilemma games occur across discrete, intra-generational time points. • Numerical simulation of the model indicates that cooperators reach fixation with far greater frequency when using schedules with prime-number period lengths. • Simulation results dovetail with the findings of a recent analytic model that confirmed a longstanding, hypothesized link between the prime numbers and the evolution of cooperation. • The findings suggest that schedules with prime-number period lengths constitute a new mechanism for the evolution of cooperation. • Viewed in concert with the findings of past-predator prey models, the results raise the possibility that cyclical behavior with prime-number period lengths might serve as an adaptive solution to a range of challenges that lifeforms face. This paper presents a model of a finite population of agents constrained to strategies that alternate between activity and inactivity (a.k.a. temporal partitioning) in a social environment where multiple one-shot prisoner's dilemma games occur across discrete, intra-generational time points. Evolutionary selection acts on agents’ behavioral dispositions to cooperate/defect and the schedules that determine when agents periodically implement that behavior. Numerical simulation of the model indicates that cooperators reach fixation with far greater frequency when using schedules with prime-number period lengths. These findings reinforce recent analytic findings that indicate a connection between the evolution of cooperation and the prime numbers, plus they offer new empirical predictions about the timing of social behavior.

Religion, parochialism and intuitive cooperation.

Religions promote cooperation, but they can also be divisive. Is religious cooperation intuitively parochial against atheists? Evidence supporting the social heuristics hypothesis (SHH) suggests that cooperation is intuitive, independent of religious group identity. We tested this prediction in a one-shot prisoner's dilemma game, where 1,280 practising Christian believers were paired with either a coreligionist or an atheist and where time limits were used to increase reliance on either intuitive or deliberated decisions. We explored another dual-process account of cooperation, the self-control account (SCA), which suggests that visceral reactions tend to be selfish and that cooperation requires deliberation. We found evidence for religious parochialism but no support for SHH's prediction of intuitive cooperation. Consistent with SCA but requiring confirmation in future studies, exploratory analyses showed that religious parochialism involves decision conflict and concern for strong reciprocity and that deliberation promotes cooperation independent of religious group identity. PROTOCOL REGISTRATION: The Stage 1 protocol for this Registered Report was accepted in principle on 28 January 2020. The protocol, as accepted by the journal, can be found at https://doi.org/10.6084/m9.figshare.12086781.v1 .

Time Pressure and In-group Favoritism in a Minimal Group Paradigm.

Based on the group heuristic model and the model of intuitive cooperation, we hypothesized that in-group favoritism would be conspicuously shown through an intuitive process. To test this hypothesis, we utilized a minimal group paradigm, which is traditionally used in social psychological studies, and manipulated decision time in a one-shot prisoner’s dilemma game to compare the cooperative contribution level toward in-group and out-group members under three conditions: intuitive, empathic deliberation, and rational deliberation. Our findings confirmed that in-group favoritism was clearly shown in the intuitive condition only, suggesting that the intuitive cooperation model may only be valid in the context of social exchange with in-group members. Additional analysis also showed that in-group favoritism disappeared for participants who had been forced into empathic or rational deliberation for decision making. The theoretical implications of the findings are discussed.

Sex differences in cooperativeness-An experiment with Buryats in Southern Siberia.

We report on an experimental study that was set up to reveal differences in the tendencies of men and women to cooperate in same-sex interactions. Former studies on this subject were mostly conducted in industrialized modern societies. In contrast, we tested the cooperation tendency among Buryats, a people from Southern Siberia of Mongolian origin. All subjects participated in (1) one iterated Public Goods Game in a group of four individuals of the same sex and (2) four one-shot Prisoner’s Dilemma games with different partners of the same sex. The interactions were in a face-to-face setting, but any intentional communication during the experiments was prohibited. We found that Buryat men were more cooperative than Buryat women in both types of same-sex interactions. In particular, the fraction of men employing a strategy of unconditional cooperation in the iterated Public Goods Game was much higher (36%) than the fraction of unconditional cooperators among women (21%). In general, the behavior of men was less context dependent than the behavior of women. In both sexes, individuals who were more cooperative in one type of game tended to be more cooperative in the other type of game. Although direct communication was prohibited, the interaction partners in the Prisoner’s Dilemma games employed the same strategy much more frequently than expected by chance. We conclude that, even among strangers, the exchange of subtle signals is sufficient to coordinate strategic decisions.

A cross-national analysis of sex differences in prisoner's dilemma games.

In a comprehensive cross-national study involving samples from 12 different countries that were representative for the adult populations in terms of age and sex (N=2,429), we found that women cooperate significantly less overall than men in fully incentivized one-shot prisoner's dilemma games. This gender gap in cooperation can be explained by the fact that women hold lower expectations regarding the cooperativeness of their anonymous interaction partners. These results contradict both the common stereotype that women are more communal, caring, emotionally expressive, and warm than men and substantial empirical evidence showing that women act more prosocially in many contexts.

Individual Characteristics vs. Experience: An Experimental Study on Cooperation in Prisoner's Dilemma.

Cooperative behavior is often assumed to depend on individuals' characteristics, such as altruism and reasoning ability. Evidence is mixed about what the precise impact of these characteristics is, as the subjects of study are generally randomly paired, generating a heterogeneous mix of the two characteristics. In this study we ex-ante create four different groups of subjects by factoring their higher or lower than the median scores in both altruism and reasoning ability. Then we use these groups in order to analyze the joint effect of the two characteristics on the individual choice of cooperating and on successful paired cooperation. Subjects belonging to each group play first 10 one-shot prisoner's dilemma (PD) games with ten random partners and then three consecutive 10-round repeated PD games with three random partners. In all games, we elicit players' beliefs regarding cooperation using an incentive compatible method. Individuals with high altruism are more optimistic about the cooperative behavior of the other player in the one-shot game. They also show higher individual cooperation and paired cooperation rates in the first repetitions of this game. Contrary to the one-shot PD games where high reasoning ability reduces the probability of playing cooperatively, the sign of the relationship is inverted in the first repeated PD game, showing that high reasoning ability individuals better adjust their behavior to the characteristics of the game they are playing. In this sense, the joint effect of reasoning ability and altruism is not linear, with reasoning ability counteracting the cooperative effect of altruism in the one-shot game and reinforcing it in the first repeated game. However, experience playing the repeated PD games takes over the two individual characteristics in explaining individual and paired cooperation. Thus, in a (PD) setting, altruism and reasoning ability significantly affect behavior in single encounters, while in repeated interactions individual and paired cooperation reach similarly high levels independently of these individual characteristics.

Social Norms and Cooperation

A theoretical framework is introduced to model social norms using the tools of psychological game theory. In the Prisoner's Dilemma Game, a preference for norm compliance can lead to cooperation arising with a positive probability, and if this preference is sufficiently strong, occurring as a pure strategy equilibrium. Thus, cooperation can arise as a social norm in a one-shot Prisoner's Dilemma Game without repeated play, communication, or sanctions.

The effect of oxytocin on cooperation in a prisoner’s dilemma depends on the social context and a person’s social value orientation

The interactionist approach to the study of exogenous oxytocin (OT) effects on prosocial behavior has emphasized the need to consider both contextual cues and individual differences. Therefore, an experiment was set up to examine the joint effect of intranasal OT, a salient social cue and the personality trait social value orientation on cooperative behavior in one-shot prisoner's dilemma games. The outcome of these mixed-motive games is known to be highly dependent on values and on social information that might reveal the partner's intent. Consistent with an a priori hypothesis, OT and social information interact significantly to affect the behavior of individuals with a proself value orientation: after prior contact with the game partner, OT enhances cooperative behavior, whereas in anonymous conditions, it exacerbates their intrinsic self-interested behavior. These effects of OT do not hold for individuals with a prosocial value orientation, whose cooperation levels appear to be more influenced by prior contact with the game partner. Follow-up hypotheses for why prosocial and proself individuals respond differently to exogenous OT were developed.

The strategy of psychopathy: primary psychopathic traits predict defection on low-value relationships

Recent evidence suggests that psychopathy is a trait continuum. This has unappreciated implications for understanding the selective advantage of psychopathic traits. Although clinical psychopathy is typically construed as a strategy of unconditional defection, subclinical psychopathy may promote strategic conditional defection, broadening the adaptive niche of psychopathy within human societies. To test this, we focus on a ubiquitous real-life source of conditional behaviour: the expected relational value of social partners, both in terms of their quality and the likely quantity of future interactions with them. We allow for conversational interaction among participants prior to their playing an unannounced, one-shot prisoner's dilemma game, which fosters naturalistic interpersonal evaluation and conditional behaviour, while controlling punishment and reputation effects. Individuals scoring higher on factor 1 (callous affect, interpersonal manipulation) of the Levenson self-report psychopathy scale defected conditionally on two kinds of low-value partners: those who interrupted them more during the conversation, and those with whom they failed to discover cues to future interaction. Both interaction effects support the hypothesis that subclinical primary psychopathy potentiates defection on those with low expected relational value. These data clarify the function and form of psychopathic traits, while highlighting adaptive variation in human social strategies.

Religious motivations for cooperation: an experimental investigation using explicit primes

The role of religion in human cooperation remains a highly contested topic. Recent studies using economic game experiments to explore this issue have been largely inconclusive, yielding a range of conflicting results. In this study, we investigate the ability of religion to promote cooperation by using explicit theological primes. In the first study, conducted in a church, we find that subjects who report a stronger connection with a Christian passage about charitable giving are subsequently more likely to cooperate in a one-shot prisoner's dilemma game. In the second study, conducted over the Internet, we find that Christian subjects are more likely to cooperate after reading a Christian passage than a neutral one. However, in the same study, we find that Hindu and secular passages have no significant effect on Christians, and that none of the passages (Christian, Hindu, or secular) have an effect on non-Christians. Our results show the potential power of explicitly religious exhortations that promote cooperation, and also their selectivity.

A behavioral analysis of altruism.

Altruistic acts have been defined, in economic terms, as "…costly acts that confer economic benefits on other individuals" (Fehr and Fischbacher, 2003). In multi-player, one-shot prisoner's dilemma games, a significant number of players behave altruistically; their behavior benefits each of the other players but is costly to them. We consider three potential explanations for such altruism. The first explanation, following a suggestion by the philosopher Derek Parfit, assumes that players devise a strategy to avoid being free-loaders-and that in the present case this strategy dictates cooperation. The second explanation says that cooperators reject the one-shot aspect of the game and behave so as to maximize reward over a series of choices extending beyond the present situation (even though reward is not maximized in the present case). This explanation assumes that people may learn to extend the boundaries of their selves socially (beyond their own skin) as well as temporally (beyond the present moment). We propose a learning mechanism for such behavior analogous to the biological, evolutionary mechanism of group selection. The third explanation assumes that people's altruism is based on a straightforward balancing of undiscounted costs to themselves against discounted benefits to others (social discounting). The three proposed explanations of altruism complement each other.

A Tag-Based Evolutionary Prisoner's Dilemma Game on Networks with Different Topologies

Researchers from many disciplines have been interested in the maintenance of cooperation in animal and human societies using the Prisoner's Dilemma game. Recent studies highlight the roles of cognitively simple agents in the evolution of cooperation who read tags to interact either discriminately or selectively with tolerably similar partners. In our study on a one-shot Prisoner's Dilemma game, artificial agents with tags and tolerance perceive dissimilarities to local neighbors to cooperate with in-group and otherwise defect. They imitate tags and learn tolerance from more successful neighbors. In terms of efficiency, society-wide cooperation can evolve even when the benefits of cooperation are relatively low. Meanwhile, tolerance however decreases as agents become homogenized. In terms of stability, parochial cooperators are gullible to the deviants - defectors displaying tolerably similar tags. We find that as the benefits of cooperation increase and the dimensions of tag space become larger, emergent societies can be more tolerant towards heterogeneous others. We also identify the effects of clustering and small-world-ness on the dynamics of tag-based parochial cooperation in spite of its fundamental vulnerability to those deviants regardless of network topology. We discuss the issue of tag mutability in search for alternative societies in which tag-based parochial cooperation is not only efficient but also robust.

You can judge a book by its cover: the sequel.: A kernel of truth in predictive cheating detection

In accordance with evolutionary models of social exchange, we suggest the possible existence of a limited predictive cheater detection module. This module enables humans, to a certain extent, to predict how willing another might be to cooperate or not. Using unknown target subjects who had played a one-shot prisoner's dilemma game earlier, we asked participants in two experiments to rate how cooperative these target subjects were. Pictures were taken of the target subjects at three different moments: a neutral-expression picture taken prior to the game, an event-related picture taken during the decision-making moment of a practice round, and an event-related picture taken during the decision-making moment of a proper round. We found that participants in the experiments could accurately discriminate noncooperative pictures from cooperative ones, but only in response to those taken during the proper round. In both neutral-expression pictures and practice-round pictures, identification rates did not exceed chance level. These findings leave room for the existence of a predictive cheater detection module that deduces someone's decision to cooperate from event-related facial expressions.

Friend or Foe?A Natural Experiment of the Prisoner's Dilemma

Abstract This study examines data drawn from the game show Friend or Foe? which is similar to the classic prisoner's dilemma tale: partnerships are endogenously determined, and players work together to earn money, after which they play a one-shot prisoner's dilemma game over large stakes: varying from $200 to (potentially) more than $22,000. The data reveal several interesting insights; perhaps most provocatively, they suggest that even though the game is played in front of an audience of millions of viewers, some of the evidence is consistent with a model of discrimination. The observed patterns of social discrimination are unanticipated, however.

An Evolutionary Explanation for the Propensity to Migrate

We explore the evolutionary dynamics of a population that consists of cooperators and defectors, wherein each member of the many pairs of players of a one-shot prisoner's dilemma game is drawn at random, and the number of descendents positively depends on the payoffs in the game. We demonstrate how an inclination to migrate may be mapped onto the overall evolutionary fitness of the cooperators. The threshold value of the inclination to migrate parameter is obtained. Intensities of migration higher than that value guarantee that in the long run, the population will consist entirely of cooperators. The threshold value is characterized by the payoff parameters lying at the base of the evolutionary dynamics.

Social Capital and Endogenous Preferences

In this paper we analyze whether social capital can emerge endogenously from a process of preference evolution. We define social capital as preferences that promote voluntary cooperation in a one-shot Prisoner's Dilemma game. We investigate how the endogenous pref- erences depend on the amount of information individuals have about each other's preferences. When there is sufficiently much information, maximal social capital emerges. In general, the level of social capital varies positively with the amount of information. Our results may add to an understanding of the factors that determine a society's ability to generate cooperative outcomes.

Reactive strategies in indirect reciprocity

Evolution of reactive strategy of indirect reciprocity is discussed, where individuals interact with others through the one-shot Prisoner's Dilemma game, changing their partners in every round. We investigate all of the reactive strategies that are stochastic, including deterministic ones as special cases. First we study adaptive dynamics of reactive strategies by assuming monomorphic population. Results are very similar to the corresponding evolutionary dynamics of direct reciprocity. The discriminating strategy, which prescribes cooperation only with those who cooperated in the previous round, cannot be an outcome of the evolution. Next we examine the case where the population includes a diversity of strategies. We find that only the mean ‘discriminatoriness’ in the population is the parameter that affects the evolutionary dynamics. The discriminating strategy works as a promoter of cooperation there. However, it is again not the end point of the evolution. This is because retaliatory defection, which was prescribed by the discriminating strategy, is regarded as another defection toward the society. These results caution that we have to reconsider the role of retaliatory defection much more carefully.

Information Preferences and Social Value Orientations in a Prisoner's Dilemma Game

This research examined the relationship between individual differences in social value orientations (cooperation, equality, individualism, and competition) and selective information preferences. One hundred and fifty-nine female college students participated in an one-shot prisoner's dilemma game, and the payoff matrices they reproduced were assessed. The results clearly showed that individuals with different social value orientations selectively processed different kinds of information contained in the payoff matrix. The observed linkage between information preferences and social value orientations implied the existence of decision making processes unique to each orientation. Further more, it was also suggested that social value orientations or individual cooperative tendencies would be closely related to their information processing complexity.