Strict or Graduated Punishment? Effect of Punishment Strictness on the Evolution of Cooperation in Continuous Public Goods Games

Abstract

Whether costly punishment encourages cooperation is one of the principal questions in studies on the evolution of cooperation and social sciences. In society, punishment helps deter people from flouting rules in institutions. Specifically, graduated punishment is a design principle for long-enduring common-pool resource institutions. In this study, we investigate whether graduated punishment can promote a higher cooperation level when each individual plays the public goods game and has the opportunity to punish others whose cooperation levels fall below the punisher’s threshold. We then examine how spatial structure affects evolutionary dynamics when each individual dies inversely proportional to the game score resulting from the social interaction and another player is randomly chosen from the population to produce offspring to fill the empty site created after a player’s death. Our evolutionary simulation outcomes demonstrate that stricter punishment promotes increased cooperation more than graduated punishment in a spatially structured population, whereas graduated punishment increases cooperation more than strict punishment when players interact with randomly chosen opponents from the population. The mathematical analysis also supports the results.

Competition of tolerant strategies in the spatial public goods game

“…Although mutual cooperation would be optimal for all involved, a higher payoff, at least in the short term, is possible by exploiting the cooperative efforts of others. An often explored remedy is to punish defectors who do not contribute to the public good [20][21][22][23][24][25][26][27][28], or to reward cooperators who do contribute to the public good [29][30][31][32][33][34][35][36]. However, the problem with both actions is that they are costly.…”

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

“…Although prosocial punishment is widespread in nature [30,31], it is unlikely that cooperators are willing to commit permanently to punishing wrongdoers. For that, the action is simply too costly, and hence some form of abstinence is likely, also to avoid unwanted retaliation.…”

Benefits of tolerance in public goods games

“…A natural reaction could be to punish the traitor, but the institution of punishment raises further questions, which sometimes just transfers the basic problem to another level [9][10][11][12][13][14]. An alternative response from betrayed cooperators could be to stop further cooperation and not to participate in the joint venture anymore.…”