Probabilistic sharing solves the problem of costly punishment

Abstract

Cooperators that refuse to participate in sanctioning defectors create the secondorder free-rider problem. Such cooperators will not be punished because they contribute to the public good, but they also eschew the costs associated with punishing defectors. Altruistic punishers-those that cooperate and punish-are at a disadvantage, and it is puzzling how such behaviour has evolved. We show that sharing the responsibility to sanction defectors rather than relying on certain individuals to do so permanently can solve the problem of costly punishment. Inspired by the fact that humans have strong but also emotional tendencies for fair play, we consider probabilistic sanctioning as the simplest way of distributing the duty. In well-mixed populations the public goods game is transformed into a coordination game with full cooperation and defection as the two stable equilibria, while in structured populations pattern formation supports additional counterintuitive solutions that are reminiscent of Parrondoʼs paradox.

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

“…In comparison with the results obtained for larger values of r as used in Ref. [27], however, the current plot features a significantly narrower p region where full cooperation is possible when α is sufficiently large. Similarly, there is a limited region of intermediate α values where cooperators that punish severely can beat defectors.…”

“…Based on these observations, in the present model we thus explore if there is an evolutionary selection among Fraction of cooperators as a function of the punishment fine α and the probability to punish p, as obtained for a low multiplication factor r = 3.5 in the original model proposed in Ref. [27], where a uniform probability to punish was assumed for all cooperators. Note that both α and p have a nonmonotonic impact on the fraction of cooperators.…”

“…However, punishment is costly, and as such it reduces the payoffs of both the defectors as well as of those that exercise the punishment, hence yielding an overall lower income and acting as a drain on social welfare. Thus, understanding the emergence of costly punishment is crucial for the evolution of cooperation [20][21][22][23][24][25][26][27].…”

“…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].…”

Dynamic Cournot duopoly games with nonlinear demand function

“…The impact of population density on the evolution of public cooperation in structured populations has been introduced by Wang et al [18]. In [19], the authors have studied the described public goods game by means of the replicator equation in well-mixed populations and by means of Monte Carlo simulations in the structured populations. The evolution of cooperation in games that describe social dilemmas has been studied by Szolnoki et al [20].…”