Evolution of altruistic punishments among heterogeneous conditional cooperators

It has been known that altruistic punishments solve the free rider problem in public goods games. Considering spatial structure and considering pure strategies significant advances have been made in understanding the evolution of altruistic punishments. However, these models have not considered key behavior regularities observed in experimental and field settings, where the individuals behave like conditional cooperators who are more willing to donate and are also more willing to punish free riders. Considering these behavioral regularities, without imposing a spatial structure on the population, I propose an evolutionary agent-based model in which agents behave like conditional cooperators, each agent's donation conditional on the difference between the number of donations in the past and the threshold value and the propensity value of the agent. Altruistic punishment depends on the difference between the threshold value of the focal agent and the randomly matched another agent. The simulations show that, for certain inflicted costs of punishments, generous altruistic punishments evolve and stabilize cooperation. The results show that, unlike previous models, it is not necessary to punish all free riders equally; it is necessary to do so in the case of the selfish free riders but not in the case of negative reciprocators.