The evolution of cooperation in dynamically spatial networks with reciprocal preference and heterogeneous linking rules

We consider a spatial generalization of evolutionary game theory in which strategies are distributed over a spatial array of sites. We assume that the strategy corresponding to a given site has local interactions with the strategies sitting on neighbouring sites, and that the strategies change if neighbouring strategies are doing better. After briefly setting the stage with a formal definition of spatial evolutionary game theory, we consider the spatial extension of the Hawk-Dove game, and we show that the results are qualitatively different from those obtained from classical evolutionary game theory. For example, the proportion of Hawks in the population is in general lower in the spatial game than in the classical one. We also consider spatial generalizations of the extensions of the Hawk-Dove game obtained by including strategies such as Retaliator and Bully. Here, too, the results from the spatial game are very different from the classical results. In particular, with space Retaliator is a much more successful strategy than one would expect from classical considerations. This suggests that, in general, spatial structure may facilitate the evolution of strategies such as Retaliator, which do not necessarily prosper classically, and which are reminiscent of the \`nice', \`provokable' and `forgiving' strategies which seem to play a central role in the evolution of cooperation. The results indicate that including spatial structure in evolutionary game theory is a fruitful extension.

Reciprocal rewards promote the evolution of cooperation in spatial prisoner's dilemma game

Evolution of cooperation in heterogeneously stochastic interactions

Other-regarding preference and the evolutionary prisoner’s dilemma on complex networks

The sustainable cooperation of innovation in industrial parks is of great significance to the sustainable development of enterprises and parks. Factors explaining enterprise innovation cooperation activities in industrial parks have attracted great attention in scholarly research. In this article, a preference-based snowdrift game model on complex networks is proposed, where different combinations of enterprise reciprocity and risk preferences are introduced into the game model. The impact of these preferences on the sustainability of cooperation in mature and less-mature parks, characterized by different network styles, is examined through simulations. The investigation reveals that reciprocity and risk preferences have an effect on the sustainable emergence of enterprise cooperation under the constraints of a loss-to-profit ratio of cooperation, network average degree, and network style. Reciprocity preferences of enterprises are shown to have a greater impact on the sustainable emergence of cooperation than risk preference in two types of parks. Additionally, this advantage is more significant in less-mature parks. The results show the positive relationships between combinations of risk aversion and reciprocity preferences and the emergence of cooperation from a long-term perspective. This study concludes with a discussion of management suggestions and policy implications. The findings shed light on the understanding of the sustainable emergence of innovation cooperation in industrial parks.

Strategy preference promotes cooperation in spatial evolutionary games

Chaos, oscillation and the evolution of indirect reciprocity in n-person games

The evolution of cooperation among selfish individuals is a fundamental issue in artificial intelligence. Recent work has revealed that interaction stochasticity can promote cooperation in evolutionary spatial prisoner’s dilemma games. Considering the players’ strategies in previous works are discrete (either cooperation or defection), we focus on the evolutionary spatial prisoner’s dilemma game with continuous strategy based on interaction stochasticity mechanism. In this paper, we find that strategy continuity do not enhance the cooperation level. The simulation results show that the cooperation level is lower if the strategies are continuous when the interaction rate is low. With higher interaction rate, the cooperation levels of continuous-strategy system and the discrete-strategy system are very close. The reason behind the phenomena is also given. Our results may shed some light on the role of continuous strategy and interaction stochasticity in the emergence and persistence of cooperation in spatial network.

The evolution of cooperation in spatial prisoner’s dilemma game with dynamic relationship-based preferential learning

The evolution of cooperation is one of the most important problems in biology. The evolutionary game theory is a useful approach for investing this problem, and some researchers have recently improved it by adding another game to the dynamics. This framework is known as “multi-games”. In this paper, we investigate the effect of the stochastic sexual interaction on the evolution of asexual cooperation. Our scenario is based on the life cycle of Dictyostelium discoideum, which has two cooperative phases: asexual fruiting body formation and sexual macrocyst formation. We assume that fruiting body formation is represented by the Prisoner’s Dilemma game, while macrocyst formation provides the constant benefits; we focus on the evolution of cooperation in fruiting body formation. Our model shows that cooperators can eliminate different mating type defectors. This occurs only if the benefit from the stochastic sexual interaction is less than from asexual cooperation. This result suggests that macrocyst formation stabilizes the evolution of cooperation in fruiting body formation to some degree. Next, we investigate the metapopulation dynamics because cooperators are eliminated by the same mating type defectors in our model. The fixation time of defectors slows down due to the stochastic sexual interaction but cooperators finally become extinct. These results suggest that a mating type works as a tag and that D. discoideum avoids the exploitation from defectors by sexual interaction.

In sociology and economics, evolutionary game theory has provided a powerful framework to illustrate the social dilemma’s problems, and many evolutionary game models are presented, such as prisoner’s dilemma game, snowdrift game, public goods game, and so on. In this paper, however, we focus on another typical pair-wise game model: Traveler’s Dilemma Game (TDG), which has been deeply investigated in economics, but less attention has been paid to this topic within the physics community. We mainly discuss the influence of strategy update rules on the evolution of cooperation in the spatial TDG, and in detail explore the role of a novel self-questioning or self-learning update mechanism in the evolution of cooperation of the TDG model on the square lattice. In our self-questioning rule, each player does not imitate the strategy state of his or her nearest neighbors and simply plays the traveler’s dilemma games twice with nearest neighbors: one is to calculate the actual payoff in the current game round; the other is to perform a virtual game which is used to obtain an intangible payoff if he or she adopts another random strategy. Then, the focal player decides to keep the current strategy or to change into that virtual strategy according to the Fermi-like dynamics. A great number of Monte Carlo simulations indicate that our self-questioning rule is a low information game decision-making mechanism which can greatly promote the evolution of cooperation for some specific conditions in the spatial TDG model. Furthermore, this novel rule can also be applied into the prisoner’s dilemma game, and likewise the behavior of cooperation can be largely enhanced. Our results are of high importance to analyze and understand the emergence of cooperation within many real social and economical systems.

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.

Effect of migration based on strategy and cost on the evolution of cooperation

The evolution of cooperation on interdependent networks is arousing increasing concern based on the fact that more and more complex systems in the real-world have been proven to be organized in the form of multi-layer networks rather than single-layer networks. In this study, we examine the effects of self-organized interdependence on the evolution and stabilization of cooperation with social dilemmas depicted by the Prisoner’s Dilemma Game (PDG) and the Public Goods Game (PGG) in which agents with the most common strategy have the chance to be rewarded proportionally to the fitness of corresponding agents belonging to the other network. We show that such a type-free rewarding rule, independent of game strategy, establishes a time-varying interdependence between two initially independent populations whereby cooperation is highly promoted as well as stabilized both in the two-player PDG and in the multi-player PGG. Majority-pressure based interdependence at stake has proven pretty neutral in regard to game strategy because it is contingent on strategy configuration rather than strategy itself, which thus gives birth to homologous communities, including cooperative as well as non-cooperative, and thereby an enhanced spatial reciprocity between non-identical networks is triggered. Of particular interest is the double-edged sword effect of network interdependence on cooperation although in most instances the heavier the interdependence, the better the evolution of cooperation. Furthermore, interpretations of the nontrivial relationship between cooperation and benchmark threshold measuring the strategy’s local popularity highlight that rewarding the minimum majority is optimal for the evolution of cooperation in such scenario. Finally, we claim our observations are also quite robust with respect to mutation.

Evolution of cooperation has been actively studied in the evolutionary computation (EC) community mainly for the iterated prisoner's dilemma (IPD) game. One of the frequently examined settings is a noisy environment where a player chooses a different action from the suggested one by its strategy with a pre-specified error probability. The use of the error probability in the IPD game usually makes the evolution of cooperation very difficult. This is because occasional defection by error disturbs mutual cooperation. In our former study, we examined the effect of the error probability on the evolution of cooperation among players with binary string strategies under various settings of memory length. Then we found that a higher average payoff was obtained by increasing the error probability from zero to a small value only when we used 7-bit binary string strategies with a memory about the opponent's previous two actions. That is, a small error probability helped the evolution of cooperation only under this particular setting. This behavior was not observed in the other settings of memory usage. In this paper, we further examine this behavior through computational experiments for a wide variety of settings of various factors. Experimental results show that this behavior is observed only under special settings of the following factors: the number of players (i.e., population size), memory length, memory usage, and a crossover operator.