Punishment in the form of shared cost promotes altruism in the cooperative dilemma games

Egoistic punishment outcompetes altruistic punishment in the spatial public goods game

The evolution of costly punishment is a puzzle due to cooperators’ second-order free-riding. Previous studies have proposed many solutions mainly focused on reducing the punishment cost or punishing second-order free riders directly or indirectly. We attempt to explain this confusion from the perspective of punishment motivation, which is why the punisher is willing to pay the cost. The answer is that the punisher is egoistic. Egoistic punishment aims to protect punishers’ own cooperative benefits shared by the defectors. In such case, egoistic punishers would pay a cost in punishing defectors and retrieve lost payoffs from defectors. Here, we examined the evolution and performance of egoistic punishment and compared it with typical altruistic punishment using classic peer-punishment and pool-punishment modes. Results showed egoistic punishment can evolve and effectively promote cooperation within a large parameter range, whether in a well-mixed or structured population, or through peer-punishment or pool-punishment modes. This result is also robust to different strategy-updating rules. The evolution under the pool-punishment mechanism is more complicated. The influence of parameters is counter-intuitive because of cycle dominance; namely, the cost is the key factor to control the level of cooperation and the fine determines the ratio of the punishers and cooperators. Compared with altruistic punishment, egoistic punishment can promote cooperation in a lower-fine and higher-cost area, especially in the pool punishment mode, and the egoistic punishers have stronger survivability. Egoistic punishers represent the natural fairness in a social system. Results revealed that focusing on individual equity can significantly promote collective cooperation. This study provides another explanation for the evolution of costly punishment.

How intergroup relation moderates group bias in Third-Party Punishment

Two experiments were conducted to investigate how intergroup relation moderates group bias in Third-Party Punishment (TPP) of selfishness. Participants competed or cooperated with the other group and then performed a TPP task in which they could reduce an allocator's benefits after paying a low cost (paying 1/3 unit deducts 1 unit of the allocator in Experiment 1, n = 76) or a high cost (paying 1 unit deducts 1 unit of the allocator in Experiment 2, n = 81). The results supported the "mere-preference hypothesis" of group bias, showing that people were more likely to tolerate their ingroups while punishing outgroups more harshly. Furthermore, when the cost was low, competition increased people's punishment toward outgroups' selfishness but not toward ingroup members, thus enlarging the group bias. When the cost was high, however, this effect disappeared, indicating that people consider a "cost-to-impact ratio" when selectively enforcing the fairness norm in intergroup conflicts. Our findings suggest how intergroup relation and cost-benefit analysis interact together to influence the group bias in TPP, providing insights into mechanisms underlying the maintenance of fairness norms and decision-making in a group context.

The public goods game with shared punishment cost in well-mixed and structured populations

Both experimental and theoretical studies have shown that punishment plays an important role in promoting cooperation. Various forms of punishment are proposed to explain why costly punishment could be maintained in the population and stabilize cooperation. Here we consider an altruistic behavior that cooperators perform cooperation and punishment simultaneously and share the punishment cost. We investigate the role of punishment cost shared among cooperators in the evolution of cooperation in public goods game. We show that the punishment can promote and stabilize cooperation when the penalty imposed on defectors is large enough compared to the punishment cost incurred by cooperators in well-mixed populations. In structured populations, cooperation could emerge under lower fine threshold and coexist with defection. However, as the penalty increases, cooperation will have a larger basin of attraction in the well-mixed population than that in the structured population. Our analytical and simulated results indicate that punishment indeed can effectively promote the evolution of cooperation. We also find that population structure can promote the coexistence of cooperation and defection but not always be beneficial to cooperation.

Individual mobility promotes punishment in evolutionary public goods games

In explaining the pressing issue in biology and social sciences how cooperation emerges in a population of self-interested individuals, researchers recently pay intensive attentions to the role altruistic punishment plays. However, as higher-order cooperators, survival of punishers is puzzling due to their extra cost in regulating norm violators. Previous works have highlighted the importance of individual mobility in promoting cooperation. Yet its effect on punishers remains to be explored. In this work we incorporate this feature into modeling the behavior of punishers, who are endowed with a choice between leaving current place or staying and punishing defectors. Results indicate that optimal mobility level of punishers is closely related to the cost of punishing. For considerably large cost, there exists medium tendency of migration which favors the survival of punishers. This holds for both the direct competition between punishers and defectors and the case where cooperators are involved, and can also be observed when various types of punishers with different mobility tendencies fight against defectors simultaneously. For cheap punishment, mobility does not provide with punishers more advantage even when they are initially rare. We hope our work provide more insight into understanding the role individual mobility plays in promoting public cooperation.