ArticleScientific reports2022
The probabilistic pool punishment proportional to the difference of payoff outperforms previous pool and peer punishment.
Article in Scientific reports, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Cooperative evolution with reward-based heterogeneous tax in spatial public goods games.iScience · 2025Article
- Cooperation without punishment.Scientific reports · 2023Article
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Abstract
The public goods game is a multiplayer version of the prisoner's dilemma game. In the public goods game, punishment on defectors is necessary to encourage cooperation. There are two types of punishment: peer punishment and pool punishment. Comparing pool punishment with peer punishment, pool punishment is disadvantageous in comparison with peer punishment because pool punishment incurs fixed costs especially if second-order free riders (those who invest in public goods but do not punish defectors) are not punished. In order to eliminate such a flaw of pool punishment, this study proposes the probabilistic pool punishment proportional to the difference of payoff. In the proposed pool punishment, each punisher pays the cost to the punishment pool with the probability proportional to the difference of payoff between his/her payoff and the average payoff of his/her opponents. Comparing the proposed pool punishment with previous pool and peer punishment, in pool punishment of previous studies, cooperators who do not punish defectors become dominant instead of pool punishers with fixed costs. However, in the proposed pool punishment, more punishers and less cooperators coexist, and such state is more robust against the invasion of defectors due to mutation than those of previous pool and peer punishment. The average payoff is also comparable to peer punishment of previous studies.
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