Co-evolution of strategies and update rules in the prisoner's dilemma game on complex networks

Cardillo, Alessio; Gómez‐Gardeñes, Jesús; Vilone, Daniele; Sánchez, Ángel

doi:10.1088/1367-2630/12/10/103034

Cited by 61 publications

(47 citation statements)

References 46 publications

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“…This, however, is understandable, since the cooperation-supporting influential players emerge only for a short period of time, but on average the overall positive effect in the stationary state is still clearly there. To conclude, it is worth pointing out that time-dependent perceptions of social dilemmas open the path toward coevolutionary models, as studied previously in the realm of evolutionary games [34,[65][66][67][68][69], and they also invite the consideration of the importance of time scales [70] in evolutionary multigames.…”

Section: Resultsmentioning

confidence: 75%

Different perceptions of social dilemmas: Evolutionary multigames in structured populations

2014

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Motivated by the fact that the same social dilemma can be perceived differently by different players, we here study evolutionary multigames in structured populations. While the core game is the weak prisoner's dilemma, a fraction of the population adopts either a positive or a negative value of the sucker's payoff, thus playing either the traditional prisoner's dilemma or the snowdrift game. We show that the higher the fraction of the population adopting a different payoff matrix the more the evolution of cooperation is promoted. The microscopic mechanism responsible for this outcome is unique to structured populations, and it is due to the payoff heterogeneity, which spontaneously introduces strong cooperative leaders that give rise to an asymmetric strategy imitation flow in favor of cooperation. We demonstrate that the reported evolutionary outcomes are robust against variations of the interaction network, and they also remain valid if players are allowed to vary which game they play over time. These results corroborate existing evidence in favor of heterogeneity-enhanced network reciprocity, and they reveal how different perceptions of social dilemmas may contribute to their resolution.

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Section: Resultsmentioning

confidence: 75%

Different perceptions of social dilemmas: Evolutionary multigames in structured populations

2014

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“…To better understand the pattern resulting from individual strategic interactions, it is thus necessary to incorporate heterogeneity into update rules and try to deal with the rising complexity. Heterogeneity in update rules can be modeled by assigning different individuals different types of update rules [43,44] or the same type of update rule but realized by different (update) functions [45][46][47][48]. For example, the pioneering work by Kirchkamp [45] explores the evolution of update rules characterized by functions with three parameters.…”

Section: Introductionmentioning

confidence: 99%

Simple property of heterogeneous aspiration dynamics: Beyond weak selection

Zhou

Vasconcelos

et al. 2018

Phys. Rev. E

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How individuals adapt their behavior in cultural evolution remains elusive. Theoretical studies have shown that the update rules chosen to model individual decision making can dramatically modify the evolutionary outcome of the population as a whole. This hints at the complexities of considering the personality of individuals in a population, where each one uses its own rule. Here, we investigate whether and how heterogeneity in the rules of behavior update alters the evolutionary outcome. We assume that individuals update behaviors by aspiration-based self-evaluation and they do so in their own ways. Under weak selection, we analytically reveal a simple property that holds for any two-strategy multi-player games in well-mixed populations and on regular graphs: the evolutionary outcome in a population with heterogeneous update rules is the weighted average of the outcomes in the corresponding homogeneous populations, and the associated weights are the frequencies of each update rule in the heterogeneous population. Beyond weak selection, we show that this property holds for public goods games. Our finding implies that heterogeneous aspiration dynamics is additive. This additivity greatly reduces the complexity induced by the underlying individual heterogeneity. Our work thus provides an efficient method to calculate evolutionary outcomes under heterogeneous update rules. *

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“…Classic examples reviewed in [38] include kin selection [39], direct and indirect reciprocity [40,41], network reciprocity [42], as well as group selection [43]. Diffusion and mobility have also been studied prominently [44][45][46][47], as were various coevolutionary models [8], involving network topology, noise, and aspiration [48][49][50][51][52][53][54][55][56], to name but a few examples. In particular, it was found that heterogeneities in the system, sometimes also referred to as diversity [57], independent of its origin, can significantly enhance cooperation levels in social dilemmas [58][59][60][61][62][63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity

et al. 2016

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Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two different games. While in well-mixed populations the random mixture of the two games is always equivalent to the average single game, in structured populations this is not always the case. We show that the outcome is in fact strongly dependent on the distance of separation of the two games in the parameter space. Effectively, this distance introduces payoff heterogeneity, and the average game is returned only if the heterogeneity is small. For higher levels of heterogeneity the distance to the average game grows, which often involves the promotion of cooperation. The presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin, and they also emphasize the importance of the population structure in amplifying facilitators of cooperation.

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Co-evolution of strategies and update rules in the prisoner's dilemma game on complex networks

Cited by 61 publications

References 46 publications

Different perceptions of social dilemmas: Evolutionary multigames in structured populations

Different perceptions of social dilemmas: Evolutionary multigames in structured populations

Simple property of heterogeneous aspiration dynamics: Beyond weak selection

Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity

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