Dilemma Game Research Articles

EVOLUTIONARY ANALYSIS OF PRISONER’S DILEMMA GAMES BASED ON MIXED RANDOM-CONFORMITY SELECTING MODEL

Inspired by the conformity phenomenon in human society, we develop a mixed neighbor selecting model adopting random-conformity rule to explore the evolutionary weak prisoner’s dilemma game. The neighbor selection rule of nodes is adjusted based on their fitness and collective influence. Under the degree-normalized payoff framework, the findings derived from Monte Carlo simulations reveal that this mixed selecting model can contribute to an impressive improvement in the Barabási-Albert network’s cooperation. In addition, experimental data obtained by investigating the game-learning skeleton indicate that, in this mixed random-conformity selecting model, normalized collective influence at moderate depth length enables influential nodes to maintain a cooperative strategy for an extended period of time. This can promote the emergence of cooperative strategies at low-degree nodes by facilitating the formation of stable cooperation-clusters centered on high-degree nodes. In addition, the normalized collective influence at excessive depth length increases the likelihood that influential nodes become defectors, thereby inhibiting the growth of cooperation-clusters and limiting cooperation.

How do reputation and conformity promote cooperation in the prisoner's dilemma?

In evolutionary games, many mechanisms have been proposed to promote cooperation between individuals and the heterogeneity of these mechanisms has been widely investigated. However, the joint effects and heterogeneity of multiple mechanisms have not been adequately studied. Here, we introduce different neighborhoods and global tags to denote different reputation and conformity types, respectively, and discuss the joint effects and heterogeneity of reputation and conformity mechanisms on promoting cooperation in the prisoner's dilemma game. Simulation results show that the joint effects of reputation and conformity mechanisms can promote cooperation effectively and the heterogeneity of these two mechanisms promotes cooperation only in certain circumstances.

Cooperative evolution under the joint influence of local popularity and global popularity

Motivated by the realistic situation that local and global information feedbacks maybe influence on the cooperative behavior, a new model of spatial prisoner’s dilemma game is proposed to consider the local popularity and global popularity based on the number of players who hold the same strategy with the central or target agent in the local and global environments. The weight of local popularity and the scaling index of the popularity are introduced to the fitness calculation. Numerical experiments show that the information of local popularity and global popularity have different effects on cooperative behavior when the scaling index of the popularity changes from positive to negative. And when the scaling index of the popularity is negative, the greater the absolute value of the scaling index is, the more conducive it is to the cooperation; but there exists the optimal value of the scaling index for the cooperative behavior when the scaling index is positive. These results maybe offer sights to a comprehensive understanding of the influence of the popularity on promoting cooperation.

Reputation-based asymmetric comparison of fitness promotes cooperation on complex networks

Reputation is elaborated in society and has a great effect on individual fitness, under which each player acquires a special fitness. An asymmetric comparison will appear when players update their strategies based on fitness and imitation dynamics. To explore the impact of the above asymmetry on the evolution of cooperation, we present a new strategy updating rule. More precisely, a player compares his/her own fitness with neighbor’s payoff when he/she updates strategy. In this paper, individual payoff is dependent on both his/her strategy and partner’s strategy; and individual fitness is calculated according to individual payoff and reputation value. Extensive simulation results illustrate that in spatial evolutionary prisoner’s dilemma game, with the help of this new strategy updating rule, the proportion of cooperators increases significantly within a wide range of parameter value. During the evolution of cooperation, asymmetric comparison of fitness can enhance network reciprocity effectively. Furthermore, a discussion on micro dynamics from the perspective of fitness is presented. To test the generality of this mechanism, we also use this new updating rule to simulate the evolution of spatial snowdrift game. In addition, the results obtained on Barabási–Albert Scale-Free network and Erdős–Rényi random graph are also shown. Our work helps to understand the evolution of cooperation and reputation.

Effects of stubborn players and noise on the evolution of cooperation in spatial prisoner’s dilemma game

The question of whether a minority of extremists can dominate the collective behavior in social dilemmas is crucial for understanding the evolution of cooperation in both human societies and animal worlds. We establish a spatial prisoner’s dilemma game model consisting of both stubborn cooperators and stubborn defectors who never change their behavior. The results reveal that a minority of stubborn players can effectively inhibit the evolution of cooperation. By introducing noise faced by stubborn players, however, we find that the inhibition of cooperation by the stubborn players can be easily canceled by the noise, which suggests a reasonable method for undermining the detrimental effects induced by extremists.

Social motives in children: Greed and fear in a social bargaining game

AbstractCooperation often coexists with defection in social interactions. Individuals may choose non‐cooperation in social dilemmas either out of fear (fear of being exploited by a non‐cooperative player) or out of greed (the desire to increase private payoff by defecting from a cooperative player). However, the developmental trajectories of such motives in social interactions remain unclear. In order to find out how fear and greed influence children's cooperative behaviors differentially, children aged 7 to 11 were tested in Study 1 using a modified repeated one‐shot prisoner's dilemma game (PDG) in which the incentives to be greedy or fearful were parametrically and independently manipulated. Results showed that children were sensitive to the greed effect at age 7 and their sensitivity was stable across middle childhood, while only 11‐year‐old children were significantly affected by fear when the greed level was low. These findings suggest that in the context of PDG, sensitivity to social threat increases with age across middle childhood especially under low temptation to exploit others, and the greed motive may be less influenced by age in this period. By continuing to use the same experiment with young adults, Study 2 revealed that young adults also demonstrated a diminished fear motive when the greed level was low in the PDG. Moreover, the sensitivity to social motives of 11‐year‐olds was comparable to the levels of young adults. Together, the present findings confirm that two different social motives underlie the development of cooperation in middle childhood.

Noise-induced sustainability of cooperation in Prisoner's Dilemma game

Based on the concept of stochastic Prisoner’s Dilemma (SPD) game in experimental economics proposed by Bereby-Meyer and Roth (Am Econ Rev 96 (2006) 1029–1042) (see also H. Kunreuther et al., Judgm. Decis. Mak. 4 (5) (2009) 363–384), the dynamical properties of the SPD game is investigated in this paper. For the non-repeated SPD game, we can see that the increase of noise intensity will not only lead to loss of the stochastic stability of the boundary state corresponding to defection but also the non-equilibrium phase transition of the quasi-stationary distribution of the system, and that the fixation probability of cooperation will increase with the increase of noise intensity. However, for the stochastic TFT-AllD game, the increase of noise intensity will lead to the loss of the stochastic stability of the two boundaries corresponding to cooperation and defection respectively, but will not lead to the non-equilibrium phase transition of the quasi-stationary distribution of the system. Moreover, as a special case of the stochastic TFT-AllD game (i.e., (m−1)(b−c)=2c), we show that the fixation probability of TFT will increase (decrease) with the increase of noise intensity if the initial frequency of TFT is less (or larger) than 1/2.

Application of the Iterated Prisoner's Dilemma and Evolutionary Game Theory in Siting Nuclear Power Plants in South Korea

The quality of an urban living environment largely depends on the planning and development of public facilities, which are often halted or delayed due to the NIMBY (not in my backyard) phenomenon. In such facilities, environmental costs are borne solely by the residents of proximity to the facility, while public goods/services produced by the facility are reaped equally by residents across the greater region, which in turn presents a complex dynamic of public and self-interest. This paper uses repeated games and evolutionary game theory to identify the optimal negotiation strategy for the government when siting nuclear power plant facilities in South Korea. This study simulated a tournament containing 36 selected iterated prisoner's dilemma strategies and considered factors including mean payoff values, payoff matrices, and Axelrod's Ecological Variant to deduce an optimal strategy. The results showed that AON2, a memory-2 strategy of direct reciprocity, would provide the most stable and high return negotiations.

Evolutionary prisoner’s dilemma game on signed networks based on structural balance theory

Evolutionary game has applications in many fields, from engineering to economics and social sciences. Applying evolutionary games to complex networks has become a hot research field. In real society, due to different personalities or interests, friendship or hostility will be established between people, and the alienation or closeness of the relationship will have a greater impact on the game. However, the existing evolutionary game studies on networks rarely comprehensively involve the multiplicity of this relationship. Trying to fill this gap, in this paper, we propose a new Signed-PD (prisoners’ dilemma) game model and derive the fixation probability formula. In our model, we introduce a trust factor and a modified Fermi function to characterize the impact of different relationships on the payoff matrix and strategy imitation respectively. Moreover, the theory of structural balance is extended by taking into account the nodes’ strategy, and a new structural balance rate calculated from energy functions is introduced to reflect structural balance changes. We explore the effect of trust factors on network game and study the impact of game parameters as well as network parameters on evolution, and investigate the impact of monotonic structural balance increasing on the evolution of cooperation in signed networks. Simulation results show that if the temptation value is below a certain threshold, the Game structural balance will change its qualitative dynamics. Furthermore, when the classical structural balance has a monotonic growth control beginning at 0, it can successfully boost the cooperator’s survival.

"On the value of modesty: How signals of status undermine cooperation": Correction to Srna et al. (2022).

Reports an error in "On the value of modesty: How signals of status undermine cooperation" by Shalena Srna, Alixandra Barasch and Deborah A. Small (Journal of Personality and Social Psychology, Advanced Online Publication, Apr 21, 2022, np). In the article, the affiliation information for Alixandra Barasch and Deborah A. Small has been updated and now appears in the author note. All versions of this article have been corrected. (The following abstract of the original article appeared in record 2022-53095-001.) The widespread demand for luxury is best understood by the social advantages of signaling status (i.e., conspicuous consumption; Veblen, 1899). In the present research, we examine the limits of this perspective by studying the implications of status signaling for cooperation. Cooperation is principally about caring for others, which is fundamentally at odds with the self-promotional nature of signaling status. Across behaviorally consequential Prisoner's Dilemma (PD) games and naturalistic scenario studies, we investigate both sides of the relationship between signaling and cooperation: (a) how people respond to others who signal status, as well as (b) the strategic choices people make about whether to signal status. In each case, we find that people recognize the relative advantage of modesty (i.e., the inverse of signaling status) and behave strategically to enable cooperation. That is, people are less likely to cooperate with partners who signal status compared to those who are modest (Studies 1 and 2), and more likely to select a modest person when cooperation is desirable (Study 3). These behaviors are consistent with inferences that status signalers are less prosocial and less prone to cooperate. Importantly, people also refrain from signaling status themselves when it is strategically beneficial to appear cooperative (Studies 4-6). Together, our findings contribute to a better understanding of the conditions under which the reputational costs of conspicuous consumption outweigh its benefits, helping integrate theoretical perspectives on strategic interpersonal dynamics, cooperation, and status signaling. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

On the value of modesty: How signals of status undermine cooperation.

[Correction Notice: An Erratum for this article was reported in Vol 123(4) of Journal of Personality and Social Psychology (see record 2023-02979-002). In the article, the affiliation information for Alixandra Barasch and Deborah A. Small has been updated and now appears in the author note. All versions of this article have been corrected.] The widespread demand for luxury is best understood by the social advantages of signaling status (i.e., conspicuous consumption; Veblen, 1899). In the present research, we examine the limits of this perspective by studying the implications of status signaling for cooperation. Cooperation is principally about caring for others, which is fundamentally at odds with the self-promotional nature of signaling status. Across behaviorally consequential Prisoner's Dilemma (PD) games and naturalistic scenario studies, we investigate both sides of the relationship between signaling and cooperation: (a) how people respond to others who signal status, as well as (b) the strategic choices people make about whether to signal status. In each case, we find that people recognize the relative advantage of modesty (i.e., the inverse of signaling status) and behave strategically to enable cooperation. That is, people are less likely to cooperate with partners who signal status compared to those who are modest (Studies 1 and 2), and more likely to select a modest person when cooperation is desirable (Study 3). These behaviors are consistent with inferences that status signalers are less prosocial and less prone to cooperate. Importantly, people also refrain from signaling status themselves when it is strategically beneficial to appear cooperative (Studies 4-6). Together, our findings contribute to a better understanding of the conditions under which the reputational costs of conspicuous consumption outweigh its benefits, helping integrate theoretical perspectives on strategic interpersonal dynamics, cooperation, and status signaling. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Does the Costless Identification of Contributors Affect the Intuitiveness of Prosocial Behavior?

Introduction/ Main Objectives: This study investigates whether relaxing the assumption of the non-anonymity of participants in an experiment of a finitely repeated public-good game with randomly matched players affects the intuitiveness of prosocial behavior. Background Problems: Various studies show that, in general, participants of social dilemma game experiments tend to be intuitive in choosing prosocial behaviour, whereas non-cooperative behavior tends to be slow. Other studies show that experiments which induced the non-anonymity of participants promote prosocial behavior, however, these studies did not impose non-anonymity on the participants. Novelty: This study aims to fill the literature gap on whether introducing non-anonymity of participants in a social dilemma game experiment may affect the intuitiveness of prosocial behavior. Research Methods: This study used a laboratory experiment of finitely repeated public-good games with randomly matched players in each stage. The main difference between the control and the treatment groups lay in the anonymity of participants in the interaction, where participants in treatment group are exposed to the photo of their opponent. Finding/Results: The results show that relaxing the anonymity setting improved the participants’ contributions to the public-good game; however, their prosocial behavior became less intuitive than non-cooperative behavior. Conclusion: This paper demonstrated an attempt to fill the gap in the literature between the intuitiveness of prosocial behaviour and the role of identity in prosocial behavior.

Hybrid learning promotes cooperation in the spatial prisoner’s dilemma game

Individuals’ strategy updating is an important factor in the spatial prisoner’s dilemma game. According to Bandura’s social learning theory, adaptive behavior adjustment involves imitating others (i.e. social-learning) and reinforcing the current behaviors based on self-feedback (i.e. self-learning). The existing researches have shown that although social learning and self-learning can promote cooperation under certain conditions, there are some deficiencies in the stability of evolution and the cooperation level. It is, therefore, worthwhile to examine whether hybrid strategy-updating can overcome the deficiencies. In this paper, we propose a hybrid strategy-updating mechanism combining social learning and self-learning. Simulation results show that the proposed hybrid strategy learning mechanism can effectively promote cooperation under appropriate parameter settings. The weight of self-learning and the aspiration of payoff have great impacts on cooperation. We find that at a low aspiration level, higher tendency towards social learning is beneficial to cooperation, while at a high level of aspiration, higher tendency towards self-learning has a significantly positive effect on cooperation. Furthermore, the dynamic mechanism of hybrid learning is explored, revealing that hybrid learning is more conducive to the maintenance of cooperation than social learning and self-learning per se. Finally, through the analysis on the evolutionary stability, we show that the hybrid learning mechanism can prevent the spread of defection when random strategy invasion happens and maintain a high cooperation level.

Reinforcement learning facilitates an optimal interaction intensity for cooperation

Our social interactions vary over time and they depend on various factors that determine our preferences and goals, both in personal and professional terms. Researches have shown that this plays an important role in promoting cooperation and prosocial behavior in general. Indeed, it is natural to assume that ties among cooperators would become stronger over time, while ties with defectors (non-cooperators) would eventually be severed. Here we introduce reinforcement learning as a determinant of adaptive interaction intensity in social dilemmas and study how this translates into the structure of the social network and its propensity to sustain cooperation. We merge the iterated prisoner’s dilemma game with the Bush-Mostelle reinforcement learning model and show that there exists a moderate switching dynamics of the interaction intensity that is optimal for the evolution of cooperation. Besides, the results of Monte Carlo simulations are further supported by the calculations of dynamical pair approximation. These observations show that reinforcement learning is sufficient for the emergence of optimal social interaction patterns that facilitate cooperation. This in turn supports the social capital hypothesis with a minimal set of assumptions that guide the self-organization of our social fabric.

Assortment and Reciprocity Mechanisms for Promotion of Cooperation in a Model of Multilevel Selection

In the study of the evolution of cooperation, many mechanisms have been proposed to help overcome the self-interested cheating that is individually optimal in the Prisoners' Dilemma game. These mechanisms include assortative or networked social interactions, other-regarding preferences considering the payoffs of others, reciprocity rules to establish cooperation as a social norm, and multilevel selection involving simultaneous competition between individuals favoring cheaters and competition between groups favoring cooperators. In this paper, we build on recent work studying PDE replicator equations for multilevel selection to understand how within-group mechanisms of assortment, other-regarding preferences, and both direct and indirect reciprocity can help to facilitate cooperation in concert with evolutionary competition between groups. We consider a group-structured population in which interactions between individuals consist of Prisoners' Dilemma games and study the dynamics of multilevel competition determined by the payoffs individuals receive when interacting according to these within-group mechanisms. We find that the presence of each of these mechanisms acts synergistically with multilevel selection for the promotion of cooperation, decreasing the strength of between-group competition required to sustain long-time cooperation and increasing the collective payoff achieved by the population. However, we find that only other-regarding preferences allow for the achievement of socially optimal collective payoffs for Prisoners' Dilemma games in which average payoff is maximized by an intermediate mix of cooperators and defectors. For the other three mechanisms, the multilevel dynamics remain susceptible to a shadow of lower-level selection, as the collective outcome fails to exceed the payoff of the all-cooperator group.

On the effect of memory on the Prisoner’s Dilemma game in correlated networks

Game theory is fundamental to understanding cooperation between agents. The Prisoner’s Dilemma is a well-known model extensively studied in complex networks. However, previous works ignore players’ memory, and the decisions about the strategies are based only on the latest games. At the same time, in real-world games, players generally consider the current situation and previous experiences when deciding their strategy. In this paper, we study how memory influences cooperation in correlated networks. We consider the evolutionary Prisoner’s Dilemma game on random and scale-free networks presenting degree–degree correlation. Through extensive simulations, we show that assortativity can improve cooperation when the temptation to defect increases. Moreover, our results suggest that including memory decreases the network structure’s influence on cooperation. Our study contributes to understanding the role of the network topology and the player’s memory on cooperation.

Intuitive thinking impedes cooperation by decreasing cooperative expectations for pro-self but not for pro-social individuals

ABSTRACT This study conducted two experiments to explore the effects of intuitive thinking and social value orientation (SVO) on cooperative behavior and assess the mediating effect of cooperative expectations. It manipulated intuitive thinking by increasing the participants’ need for cognitive closure, classified SVO using the triple-dominance measure, measured cooperative behavior using the prisoner’s dilemma game, and considered cooperative expectations based on participants’ assessments of the cooperativeness of their counterparts. Both experiments showed that intuitive thinking increased and decreased the cooperation of pro-social and pro-self individuals, respectively. In pro-self individuals, cooperative expectations mediated the effect of intuitive thinking on cooperation.

Effect of state transition triggered by reinforcement learning in evolutionary prisoner’s dilemma game

Cooperative behavior is essential for conflicts between collective and individual benefits, and evolutionary game theory provides a key framework to solve this problem. Decision-making of human or automata agent occurs not only in a static environment, but also in the dynamic interactive environment. Since the reinforcement learning algorithm is well performed at explaining the problem in regard to state, action, and environment, we propose a game model with individual state transition which is influenced by the self-regarding Q-learning algorithm. In detail, we at the first time investigate a two-state two-action game, where agents can choose either to participate in the network game (i.e., active agent) or to cut off all the links based on its Q-table (i.e., inactive agent), involving in a dynamic interactive environment. Through numerical simulations, it is shown that cooperation can reach the maximal level in the moderate value space of fixed reward obtained by inactive agents. In particular, long-term expectations and large learning rates are more productive in promoting cooperation. Furthermore, when the dynamic interactive environment reaches a stable state, the number of active neighbors of active cooperators is larger than that of active defectors, which is further larger than the number of active neighbors of inactive agents. Finally, we testify the results of theoretical analysis from the perspective of state transition.

Controlling Conditional Expectations by Zero-Determinant Strategies

Zero-determinant strategies are memory-one strategies in repeated games which unilaterally enforce linear relations between expected payoffs of players. Recently, the concept of zero-determinant strategies was extended to the class of memory-n strategies with nge 1, which enables more complicated control of payoffs by one player. However, what we can do by memory-n zero-determinant strategies is still not clear. Here, we show that memory-n zero-determinant strategies in repeated games can be used to control conditional expectations of payoffs. Equivalently, they can be used to control expected payoffs in biased ensembles, where a history of action profiles with large value of bias function is more weighted. Controlling conditional expectations of payoffs is useful for strengthening zero-determinant strategies, because players can choose conditions in such a way that only unfavorable action profiles to one player are contained in the conditions. We provide several examples of memory-n zero-determinant strategies in the repeated prisoner’s dilemma game. We also explain that a deformed version of zero-determinant strategies is easily extended to the memory-n case.

The Approach Repetition Rate Efficiency in Memorable Iterated Prisoner Dilemma Game

The Approach Repetition Rate Efficiency in Memorable Iterated Prisoner Dilemma Game