Punishment based on public benefit fund significantly promotes cooperation.

Recently, the authors proposed a quantum prisoner’s dilemma game based on the spatial game of Nowak and May, and showed that the game can be played classically. By using this idea, we proposed three generalized prisoner’s dilemma (GPD, for short) games based on the weak Prisoner’s dilemma game, the full prisoner’s dilemma game and the normalized Prisoner’s dilemma game, written by GPDW, GPDF and GPDN respectively. Our games consist of two players, each of which has three strategies: cooperator (C), defector (D) and super cooperator (denoted by Q), and have a parameter γ to measure the entangled relationship between the two players. We found that our generalised prisoner’s dilemma games have new Nash equilibrium principles, that entanglement is the principle of emergence and convergence (i.e., guaranteed emergence) of super cooperation in evolutions of our generalised prisoner’s dilemma games on scale-free networks, that entanglement provides a threshold for a phase transition of super cooperation in evolutions of our generalised prisoner’s dilemma games on scale-free networks, that the role of heterogeneity of the scale-free networks in cooperations and super cooperations is very limited, and that well-defined structures of scale-free networks allow coexistence of cooperators and super cooperators in the evolutions of the weak version of our generalised prisoner’s dilemma games.

Locus of control and learning to cooperate in a prisoner's dilemma game

Female college students first played a pseudo-prisoner's dilemma (PPD) game with the experimenter, who followed a fixed strategy. In the first experiment the experimenter's strategies for different groups of subjects were: (a) play tit-for-tat; (b) play randomly; (c) always cooperate; (d) always defect (‘cooperation’ and ‘defection’, defined as in an actual prisoner's dilemma game). Only the tit-for-tat group increased cooperation over trials; other groups decreased cooperation. After playing the PPD with the experimenter, subjects played an actual prisoner's dilemma (PD) game with each other. In the PD game, subjects began cooperating moderately but cooperation deteriorated regardless of what the experimenter's strategy had been in the earlier (PPD) game. In a second experiment, subjects again played a PPD game with the experimenter and then played a PD game with each other. Half played one trial at a time as in the first experiment while half played in patterns of four trials at a time. In the PD game, patterning of trials retarded the development of mutual defection regardless of previous experience. The cooperation-preserving effect of patterning of trials in this social task is compared with similar effects on individual tasks involving self-control and risk-aversion. © 1998 John Wiley & Sons, Ltd.

7 - Experiments With Prisoner's Dilemma and Related Games

The present research involved an examination of interindividual-intergroup discontinuity in the context of three different generalizations of the prisoner's dilemma game (PDG). (Interindividual-intergroup discontinuity is the tendency of intergroup relations to be more competitive and less cooperative than interindividual relations.) Experiment 1 used a multi-prisoner's dilemma (MPD) game to compare interaction between three individuals with interaction between three groups. Results revealed just as much discontinuity between three players (MPD) as between two players (PDG). Experiment 2 used the approach of n-person games to examine two further generalizations from the PDG. One generalization involved the intergroup public goods (IPG) game, and the other the intergroup prisoner's dilemma (IPD) game. With both games, it was found that groups were more competitive than individuals. It was also found that discussion between groups is characterized by a higher frequency of fear and greed statements than is discussion between individuals.

A simple rule of direct reciprocity leads to the stable coexistence of cooperation and defection in the Prisoner's Dilemma game

It was known that cooperation of evolutionary prisoner's dilemma games fails to emerge in homogenous networks such as random graphs. Here we proposed a quantum prisoner's dilemma game. The game consists of two players, in which each player has three choices of strategy: cooperator (C), defector (D) and super cooperator (denoted by Q). We found that quantum entanglement guarantees emergence of a new cooperation, the super cooperation of the quantum prisoner's dilemma games, and that entanglement is the mechanism of guaranteed emergence of cooperation of evolutionary prisoner's dilemma games on networks. We showed that for a game with temptation b, there exists a threshold for a measurement of entanglement, beyond which, (super) cooperation of evolutionary quantum prisoner's dilemma games is guaranteed to quickly emerge, giving rise to stochastic convergence of the cooperations, that if the entanglement degree γ is less than the threshold , then the equilibrium frequency of cooperations of the games is positively correlated to the entanglement degree γ, and that if γ is less than and b is beyond some boundary, then the equilibrium frequency of cooperations of the games on random graphs decreases as the average degree of the graphs increases.

The relationship between temporal discounting and the prisoner's dilemma game in intranasal abusers of prescription opioids

Abstract.When the presence of unexploited/ree riding opportunities within organizations is considered a sign of cooperation among employees, a repeated prisoner's dilemma game may be used as an explanation. In this paper, arguments against sole reliance on the repeated prisoner's dilemma game for explaining cooperation within the firm are set forth. Some overlooked reasons for explaining cooperation are offered.

How does conformity promote the enhancement of cooperation in the network reciprocity in spatial prisoner's dilemma games?

A number of authors have proposed that preference for a larger, delayed reward in delay discounting is similar to cooperation in a repeated prisoner's dilemma game versus tit-for-tat. This proposal was examined by correlating delay-discounting (Experiment 1) and probability-discounting (Experiment 2) rates for hypothetical monetary gains and losses with performance in a repeated prisoner's dilemma game. Correlations between rate of delay discounting (discounting parameters and area under the curve) and proportion of cooperation in the repeated prisoner's dilemma game versus tit-for-tat were significant across three magnitudes, and correlations were generally higher with discounting for losses than with that for gains. As was expected, correlations between rate of delay discounting and performance versus a random strategy in the prisoner's dilemma game were not significant. Correlations between rate of probability-discounting and cooperation rate in a repeated prisoner's dilemma game versus neither a tit-for-tat nor a random strategy were significant.

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

Heterogeneity reproductive ability promotes cooperation in spatial prisoner's dilemma game

A Critical Analysis of Research Utilizing the Prisoner's Dilemma Paradigm for the Study of Bargaining

The prisoner's dilemma (PD) game is a simple model for understanding cooperative patterns in complex systems. Here, we study a PD game problem in scale-free networks containing hierarchically organized modules and controllable shortcuts connecting separated hubs. We find that cooperator clusters exhibit a percolation transition in the parameter space (p,b), where p is the occupation probability of shortcuts and b is the temptation payoff in the PD game. The cluster size distribution follows a power law at the transition point. Such a critical behavior, resulting from the combined effect of stochastic processes in the PD game and the heterogeneity of complex network structure, illustrates diversities arising in social relationships and in forming cooperator groups in real-world systems.