Retaliation and the role for punishment in the evolution of cooperation

Wolff, Irenaeus

doi:10.1016/j.jtbi.2012.09.012

Cited by 9 publications

(3 citation statements)

References 45 publications

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“…The previous studies (Wolff (2012); Helbing et al (2010a)) have stressed that the random mutation can create some extent of strategy-mixing, and the introduction of mutation enable us to yield the deterministic replicator dynamics in the limit of frequent sampling in the absence of mutations in a large population (Dercole et al (2013)). Moreover, in the presence of the mutation, even though altruistic punishers and selfish punishers evolving from random mutation frequencies cannot stabilise full cooperation (Wolff (2012)), they could have more chances to touch the first-order free riders (D) and second-order free riders (C) (Helbing et al (2010a)) to suppress them. The performance of punishment would be thus enhanced by random mutation.…”

Section: Modelmentioning

confidence: 99%

Selfish punishment with avoiding mechanism can alleviate both first-order and second-order social dilemma

Cui

2014

Journal of Theoretical Biology

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Punishment, especially selfish punishment, has recently been identified as a potent promoter in sustaining or even enhancing the cooperation among unrelated individuals. However, without other key mechanisms, the first-order social dilemma and second-order social dilemma are still two enduring conundrums in biology and the social sciences even with the presence of punishment. In the present study, we investigate a spatial evolutionary four-strategy prisoner׳s dilemma game model with avoiding mechanism, where the four strategies are cooperation, defection, altruistic and selfish punishment. By introducing the low level of random mutation of strategies, we demonstrate that the presence of selfish punishment with avoiding mechanism can alleviate the two kinds of social dilemmas for various parametrizations. In addition, we propose an extended pair approximation method, whose solutions can essentially estimate the dynamical behaviors and final evolutionary frequencies of the four strategies. At last, considering the analogy between our model and the classical Lotka-Volterra system, we introduce interaction webs based on the spatial replicator dynamics and the transformed payoff matrix to qualitatively characterize the emergent co-exist strategy phases, and its validity are supported by extensive simulations.

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Section: Modelmentioning

confidence: 99%

Selfish punishment with avoiding mechanism can alleviate both first-order and second-order social dilemma

Cui

2014

Journal of Theoretical Biology

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“…For that, the action is simply too costly, and hence some form of abstinence is likely, also to avoid unwanted retaliation. Several research groups * xiaojiechen@uestc.edu.cn † szolnoki@mfa.kfki.hu ‡ matjaz.perc@uni-mb.si have recently investigated these and related up and down sides of punishment [27,[32][33][34][35][36]. For example, it was shown that cooperators punish defectors selectively depending on their current personal emotions, even if the number of defectors is large [29].…”

Section: Introductionmentioning

confidence: 99%

Competition and cooperation among different punishing strategies in the spatial public goods game

2015

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Inspired by the fact that people have diverse propensities to punish wrongdoers, we study a spatial public goods game with defectors and different types of punishing cooperators. During the game, cooperators punish defectors with class-specific probabilities and subsequently share the associated costs of sanctioning. We show that in the presence of different punishing cooperators the highest level of public cooperation is always attainable through a selection mechanism. Interestingly, the selection does not necessarily favor the evolution of punishers who would be able to prevail on their own against the defectors, nor does it always hinder the evolution of punishers who would be unable to prevail on their own. Instead, the evolutionary success of punishing strategies depends sensitively on their invasion velocities, which in turn reveals fascinating examples of both competition and cooperation among them. Furthermore, we show that under favorable conditions, when punishment is not strictly necessary for the maintenance of public cooperation, the less aggressive, mild form of sanctioning is the sole victor of the selection process. Our work reveals that natural strategy selection cannot only promote, but sometimes also hinders competition among prosocial strategies.

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“…Over the past few decades, evolutionary game theory has provided a powerful framework to address the evolution of cooperation [10][11][12][13][14][15][16][17]. In order to better investigate the cooperative behavior within the selfish population, many mechanisms have been proposed, such as reputation [18][19][20][21], reward [22,23], punishment [24][25][26], memory [27][28][29], migration [30][31][32][33], noise [34][35][36], interactive Inspired by the daily lifestyle, an individual may take different ways or attitudes towards his friends. Within the evolutionary game theory, it can be reflected that the vast majority of individuals update their strategies towards neighbors differently, rather than being uniformly random [42].…”

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confidence: 99%

Evolution of cooperation under the aspiration-based interactive diversity in the spatial prisoner's dilemma game

Gao¹,

Wang²,

Zhang³

et al. 2022

EPL

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In the real world, an individual may have different attitudes towards his friends. From the perspective of the evolutionary game theory, it can be reflected that individuals tend to adopt different strategies towards different opponents, which can be defined as the interactive diversity. Up to now, the evolution of cooperation with individual characteristics under the interactive diversity still needs to be further explored. Herein, under the framework of interactive diversity, we consider the influence of individual aspiration on the evolution of cooperation in the prisoner's dilemma game, in which the parameter α is introduced to represent the individual aspiration level and used to measure individual satisfaction to the neighbors in the process of strategy updating. We find that for different temptations to defect, there is an optimal interval about the aspiration level α, which can significantly promote the evolution of cooperation. Moreover, we observe that the phase transition phenomenon for the cooperation exists, and the reason for this phenomenon to occur is also analyzed from the microscopic views. Overall, the current findings can provide some interesting insights into the role of individual aspiration and the interactive diversity in solving social dilemmas.

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Retaliation and the role for punishment in the evolution of cooperation

Cited by 9 publications

References 45 publications

Selfish punishment with avoiding mechanism can alleviate both first-order and second-order social dilemma

Selfish punishment with avoiding mechanism can alleviate both first-order and second-order social dilemma

Competition and cooperation among different punishing strategies in the spatial public goods game

Evolution of cooperation under the aspiration-based interactive diversity in the spatial prisoner's dilemma game

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