The impact of total game benefits redistribution on cooperative evolution

A sovereignty strategy is proposed herein, grounded in cooperation, individual investment costs, and the capacity to redistribute the total benefits of both parties in the game. Sovereignty strategies can take part of the benefits from individuals using defection strategies, thereby suppressing the free-riding incentives of defectors. Accordingly, an evolutionary model of the Prisoner's Dilemma is constructed, consisting of cooperation strategy, defection strategy, and sovereignty strategy. The results show that regarding the degree of benefits distribution right, there exists a threshold. When the regulation degree increases within this threshold range, it promotes the emergence of sovereignty strategy until their level reaches a maximum, cooperators will also increase accordingly.When the right degree exceeds the threshold, the inhibitory effect on sovereignty strategy becomes increasingly apparent with further increases. The benefits of the cooperators will be divided by the sovereignty, resulting in fewer cooperators. As for the defection temptation, when it increases, the proportion of sovereignty strategy rises. Additionally, when the right degree is moderate, there is a threshold for defection temptation. Within this threshold, an increase in temptation reduces defection strategy while increasing sovereignty and cooperation strategy; beyond the threshold, an increase in temptation gradually increase sovereigns, and cooperators are attacked by both defectors and sovereigns, leading to a decrease in cooperators. Regarding investment costs, as they increase, the proportions of both sovereignty and cooperation strategies decrease. The model constructed in this paper and the conclusions drawn provide a theoretical reference for the design of benefits distribution right in the context of a Prisoner's Dilemma to facilitate the evolution of cooperation.