Evolution of altruistic punishments among heterogeneous conditional cooperators

Abstract

Although altruistic punishments solve the free rider problem in repeated public good games, it has been a puzzle why altruistic punishers willing to incur personal costs in order to improve the group benefits. It has been shown that when the population consists of a finite set of pure strategies along with altruistic punishers, altruistic punishments evolve in the population. These models the population consists of a finite set of strategies and the strategies do not depend on the past strategies of the population. Unlike assumptions made in these models, the population is heterogeneous in their conditional cooperative strategies and the individuals who are more willing to donate also are more willing to punish the free riders. I propose an evolutionary agent-based model, each agent’s donation depends on the difference between the number of donations in the past and the threshold value and a propensity value. Altruistic punishment depends on the difference between the threshold value of altruistic punisher and random matched another agent. The proposed model overcomes the unrealistic assumptions made in the previous models and altruistic punishments evolve for a large set of parameters. The simulations show that, for certain inflicted costs of punishments, generous altruistic punishments evolve in the population and establish stable cooperation. The conditional nature of cooperation implies that, unlike previous models, it is not necessary to punish all free riders equally, but it is necessary to do so in the case of the selfish free riders but not in the case of negative reciprocators.