The influence of the heterogeneities of social institutions and individuals’ tendency to establish social institutions on cooperation

Punishment and reward are fundamental in promoting cooperation within human societies. However, as punishment incurs costs, it is crucial to determine who should bear these costs and what specific forms of punishment should be implemented. In previous research, the primary modes of punishment have involved punishers incurring costs to directly punish defectors and pro-social individuals supporting social institutions that indirectly sanction anti-social behaviors. Additionally, individual altruistic actions can foster social cooperation, but it is often limited by what is referred to as “second-order free-riding” behaviors exhibited by regular cooperators. To address this issue, this paper proposes a spatial prisoner’s dilemma model incorporating heterogeneous social institutions and heterogeneous attitudes of individuals towards social institutions, where pro-social individuals establish separate social punishment and social security institutions for self-support and punishment. Similarly, anti-social individuals may establish anti-social punishment institutions for counteraction. The selective investment mechanism is expected to reduce or avoid the second-order free-riding behavior to some extent. Simultaneously, to address the waste of institutional resources caused by the inability of individuals to pay high penalties, a non-wasteful model with an upper limit on punishments has also been proposed. The results of simulation and dynamic analysis indicate that heterogeneities of social institutions and individuals’ tendency to establish social institutions not only can facilitate the evolution of pro-social groups, but also suppress effectively second-order free-riding behavior in the system. Moreover, it does not induce higher order free-riding behavior. Therefore, it can greatly improve the level and environment of cooperation in the system.