Abstract
Prosocial punishment has been proved to be a powerful mean to promote cooperation. Recent studies have found that social exclusion, which indeed can be regarded as a kind of punishment, can also support cooperation. However, if prosocial punishment and exclusion are both present, it is still unclear which strategy is more advantageous to curb free-riders. Here we first study the direct competition between different types of punishment and exclusion. We find that pool (peer) exclusion can always outperform pool (peer) punishment both in the optional and in the compulsory public goods game, no matter whether second-order sanctioning is considered or not. Furthermore, peer exclusion does better than pool exclusion both in the optional and in the compulsory game, but the situation is reversed in the presence of second-order exclusion. Finally, we extend the competition among all possible sanctioning strategies and find that peer exclusion can outperform all other strategies in the absence of second-order exclusion and punishment, while pool exclusion prevails when second-order sanctioning is possible. Our results demonstrate that exclusion is a more powerful strategy than punishment for the resolution of social dilemmas.
Highlights
To summarize our present knowledge, both prosocial exclusion and prosocial punishment have been proved to be effective ways for promoting cooperation, but their systematic comparison is still missing
We investigate the competition between peer exclusion and peer punishment, and find that peer exclusion is evolutionarily advantageous over peer punishment both in the optional and in the compulsory public goods game (PGG), independently of the choice of second-order sanctioning
We have studied the competitions between costly punishments and exclusions in finite populations playing the PGG by using different scenarios
Summary
We first study the direct competition between pool exclusion and pool punishment in the optional PGG In this scenario, there are five available strategies in the population fulfilling the constraint X +Y +Z +F +V =M. The second largest population is formed by pool-excluders followed by defectors and loners, while pool-punishers can make up the smallest fraction, or can be detected with the smallest probability. This result suggests that pool exclusion is more effective against defection and has an evolutionary advantage over pool-punishment strategy. In the strong imitation (κ →∞) limit the long-run frequencies in the [X, Y, Z, F, V] subpopulations are
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