Benefits of asynchronous exclusion for the evolution of cooperation in stochastic evolutionary optional public goods games

Joint effects of voluntary participation and group selection on the evolution of altruistic punishment

It is puzzling how altruistic punishment of defectors can evolve in large groups of nonrelatives, since punishers should voluntarily bear individual costs of punishing to benefit those who do not pay the costs. Although two distinct mechanisms have been proposed to explain the puzzle, namely voluntary participation and group-level competition and selection, insights into their joint effects have been less clear. Here we investigated what could be combined effects of these two mechanisms on the evolution of altruistic punishment and how these effects can vary with nonparticipants’ individual payoff and group size. We modelled altruistic punishers as those who contribute to a public good and impose a fine on each defector, i.e., they are neither pure punishers nor excluders. Our simulation results show that voluntary participation has negative effects on the evolution of cooperation in small groups regardless of nonparticipants’ payoffs, while in large groups it has positive effects within only a limited range of nonparticipants’ payoff. We discuss that such asymmetric effects could be explained by evolutionary forces emerging from voluntary participation. Lastly, we suggest that insights from social science disciplines studying the exit option could enrich voluntary participation models.

The evolution of cooperation in spatial public goods game with conditional peer exclusion

Social exclusion can prevent free riders from participating in social activities and deprive them of sharing cooperative benefits, which is an effective mechanism for the evolution of cooperation. However, traditional peer-exclusion strategies are unconditional, and as long as there are defectors in the group, they will pay a cost to exclude the defectors. In reality, one of the reasons for the complexity of these strategies is that individuals may react differently depending on the environment in which they are located. Based on this consideration, we introduce a kind of conditional peer-exclusion strategy in the spatial public goods game model. Specifically, the behavior of conditional exclusion depends on the number of defectors in the group and can be adjusted by a tolerance parameter. Only if the number of defectors in the group exceeds the tolerance threshold, conditional exclusion can be triggered to exclude defectors. We explore the effects of parameters such as tolerance, exclusion cost, and probability of exclusion success on the evolution of cooperation. Simulation results confirmed that conditional exclusion can greatly reduce the threshold values of the synergy factor above which cooperation can emerge. Especially, when the tolerance is low, very small synergy factors can promote the population to achieve a high level of cooperation. Moreover, even if the probability of exclusion success is low, or the unit exclusion cost is relatively high, conditional exclusion is effective in promoting cooperation. These results allow us to better understand the role of exclusion strategies in the emergence of cooperation.