Cooperation in PD Games: Fear, Greed, and History of Play

The main purpose of this study is to apply the "selective play paradigm" to explain how cooperation emerges in one-shot prisoner's dilemmas. A unique feature of the selective play paradigm is the option for not playing a PD game. For this purpose, a computer simulation of 100-actor groups was conducted. At the beginning of each replication, each simulated actor was randomly assigned to one of eleven levels of trust, which indicates the actor's estimate of the overall cooperation rate in the group. Each simulated actor, then, decided whether or not to interact with the previous partner based on the calculated expected gains from interacting with one of the other partners. Results of the simulation show that: (1) when substantial opportunity costs exist, having a high level of trust benefits the actor; (2) the above effect of trust depends on the actor's cooperativeness in PD games; (3) but does not depend on the overall cooperation rate in the group.

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.

Social Pressures in the one-shot Prisoner's Dilemma

Cooperators can invade an incumbent population of defectors when one-shot prisoner's dilemmas occur multiple times within a generation

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 evolution of one-shot cooperation: An experiment

Theories of choice in economics typically assume that interacting agents act individualistically and maximize their own utility. Specifically, game theory proposes that rational players should defect in one-shot prisoners' dilemmas (PD). Defection also appears to be the inevitable outcome for agents who learn by reinforcement of past choices, because whatever the other player does, defection leads to greater reinforcement on each trial. In a computer simulation and 4 experiments, the authors show that, apparently paradoxically, when players' choices are correlated by an exogenous factor (here, the cooperativeness of the specific PD chosen), people obtain greater average reinforcement for cooperating, which can sustain cooperation. This effect arises from a well-known statistical paradox, Simpson's paradox. The authors speculate that this effect may be relevant to aspects of real-world human cooperative behavior.

Efficiency in evolutionary games: Darwin, nash and the secret handshake

Cooperation Increases with the Benefit-to-Cost Ratio in One-Shot Prisoner's Dilemma Experiments

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.Prisoner's Dilemma Game, Tags, Parochial Cooperation, Clustering, Small-World-Ness, NetLogo How can society-wide cooperation at the global level emerge from local interactions of people who read observable markers and have limited tolerance for cooperating with others who they see as different from themselves, then?Such parochial cooperation stops at group boundaries.Within-group cooperation and between-group non-cooperation do not result in globalized cooperation.High levels of cooperation in parochial societies are possible either when their members look very alike in spite of low levels of tolerance or when more tolerant agents constitute a vast majority of the population.Which societies will emerge under selection pressure -if human agents learn tolerance and imitate makers from more successful others?Parochial cooperators can recognize each other by "secret handshaking" ( Robson 1990) to share the disproportionate benefits of in-group favoritism.But, emergent cooperative societies may be no longer stable in the presence of defectors who learn signals among cooperators.The failure of secret handshaking may lead to serious downward spirals of cooperation.Societies in which less parochial residents trust heterogeneous others are desirable concerning the diversity of tolerance and markers.However, more tolerant societies are more easily vulnerable to immigrated deviants displaying similar markers without providing any help.How can cooperation on the basis of similarity be stable in spite of repeated attacks by defectors with tolerably similar markers? Mechanisms of CooperationImagine the very simple situation that if Person A helps Person B at a cost c, Person B receives a benefit b.This helping game is the same as the Prisoner's Dilemma game if the benefit-to-cost ratio is bigger than 1, where mutual cooperation is Pareto optimal, but both individuals are worse off.Several mechanisms have been proposed to explain the evolution of cooperation in human societies.According to the theory of kin selection ( Hamilton 1964), altruism can be preferred if its benefit-to-cost ratio is higher than the probability of sharing a gene (Nowak 2006).This cannot be extended to cooperative behavior among genetically unrelated people, however.Direct reciprocity (Axelrod 1984) leads to cooperation if the benefit-to-cost ratio is higher than the possibility of another encounter between the same two individuals (Nowak 2006).It is not applicable to sizeable populations consisting of those who rarely interact with the same partners.It is a theoretical and empirical puzzle to explain the emergence of cooperation and its maintenance in the setting of one-shot interaction without reciprocity.Local interaction alone can facilitate society-wide cooperation in a one-shot Prisoner's Dilemma game among multiple agents ( Nowak and May 1992).Agents play the game with adjacent neighbors, and then parents produce offspring in the neighborhood in proportion to their

The critical mass effect is a prevailing topic in the study of complex systems. Recent research indicates that a committed minority of cooperators, unwavering in their beliefs and consistently maintaining cooperation, can effectively foster widespread cooperation in social dilemma games. However, achieving a critical mass of cooperation in the one-shot prisoner's dilemma requires stricter conditions. The underlying mechanism behind this effect remains unclear, particularly in the context of repeated interactions. This work aims to investigate the influence of a committed minority on cooperation in the iterated prisoner's dilemma game, a widely studied model of repeated interactions between individuals confronting a social dilemma. In contrast to previous findings, we identify tipping points for both well-mixed and structured populations. Our findings demonstrate that a committed minority of unconditional cooperators can induce full cooperation under weak imitation conditions. Conversely, a committed minority of conditional cooperators, who employ extortion strategy, can promote widespread cooperation under strong imitation conditions. These results are consistent across various network topologies and imitation rules, suggesting that critical mass effects may be a universal principle in social dilemma games. Moreover, we discovered that an excessive density of committed extortioners can hinder cooperation in structured populations. This research advances our understanding of the role of committed minorities in shaping social behavior and provides valuable insights into cooperation dynamics. Published by the American Physical Society 2024

Cooperation in one-shot anonymous interactions is a widely documented aspect of human behaviour. Here we shed light on the motivations behind this behaviour by experimentally exploring cooperation in a one-shot continuous-strategy Prisoner's Dilemma (i.e. one-shot two-player Public Goods Game). We examine the distribution of cooperation amounts, and how that distribution varies based on the benefit-to-cost ratio of cooperation (b/c). Interestingly, we find a trimodal distribution at all b/c values investigated. Increasing b/c decreases the fraction of participants engaging in zero cooperation and increases the fraction engaging in maximal cooperation, suggesting a role for efficiency concerns. However, a substantial fraction of participants consistently engage in 50% cooperation regardless of b/c. The presence of these persistent 50% cooperators is surprising, and not easily explained by standard models of social preferences. We present evidence that this behaviour is a result of social preferences guided by simple decision heuristics, rather than the rational examination of payoffs assumed by most social preference models. We also find a strong correlation between play in the Prisoner's Dilemma and in a subsequent Dictator Game, confirming previous findings suggesting a common prosocial motivation underlying altruism and cooperation.

A Non-Cooperative Pareto-Efficient Solution to the One-Shot Prisoner’s Dilemma

The chapter shows that a simple heuristic, which directs cooperation toward economic equals and defects on other individuals, facilitates cooperation in social environments where individuals engage in multiple, nonrepeated prisoner's dilemma games with partners whom they know little about. The heuristic produces successful cooperation due to its ability to infer whether or not its partner in a social encounter employs the same heuristic—not whether that partner is cooperative per se. As noted in previous research and elaborated upon here, this property prevents the heuristic from suffering exploitation and it also impedes easily exploited cooperative strategies from proliferating in conditions of ubiquitous cooperation. These aspects of the strategy, furthermore, yield insight into the environments in which the heuristic fosters high levels of cooperation. The heuristic best succeeds at producing cooperation in social environments where agents involve themselves in a moderate number of low information, one-shot prisoner's dilemma games per generation. As the number of such encounters increases per generation, the strategy more frequently defects on its social partners. Nonetheless, the heuristic cultivates cooperation in social environments where interactions are not repeated, opportunities for punishment do not exist, and agents have no direct information about their partner's past cooperativeness.

By applying the“illusion of control”hypothesis (Karp et al., 1993), originally developed to explain ingroup favoritism in the minimal group experiments, to a prisoner's dilemma (PD) situation, we predicted that the cooperation rate of players would be affected by their illusion of control. We used a sequential PD in which one player decides before the other does to maximize and minimize feasibility of illusion of control. Specifically, the following three hypotheses were successfully tested. Hypothesis 1: The decision of the second player in a sequential PD would be affected by the choice of the first player, cooperating with the cooperative first player and defecting with the defective first player. Hypothesis 2: Compared to the players of ordinary simultaneous one-shot PD (simultaneous condition), the player who decides first and whose decision is informed to the second player before the latter makes his/her decision would feel controllability over the second player and thus would cooperate more. Hypothesis 3: Compared to the simltaneous condition, players uwould cooperate less when they know (without being informed of the first player's choice) that the first player has already made his/her decision. The second experiment was conducted to replicate Hypothesis 3, the most important hypothesis of the three. The hypothesis was also supported in the second experiment.