Research on Repeated Quantum Games with Public Goods under Strong Reciprocity

Abstract

We developed a repeated quantum game of public goods by using quantum entanglement and strong reciprocity mechanisms. Utilizing the framework of quantum game analysis, a comparative investigation incorporating both entangled and non-entangled states reveals that the player will choose a fully cooperative strategy when the expected cooperation strategy of the competitor exceeds a certain threshold. When the entanglement of states is not considered, the prisoner’s dilemma still exists, and the cooperating party must bear the cost of defactoring the quantum strategy themselves; when considering the entanglement of states, the benefits of both parties in the game are closely related, forming a community of benefits. By signing a strong reciprocity contract, the degree of cooperation between the game parties can be considered using the strong reciprocity entanglement contract mechanism. The party striving to cooperate does not have to bear the risk of the other party’s defector, and to some extent, it can solve the prisoner’s dilemma problem. Finally, taking the public goods green planting industry project as an example, by jointly entrusting a third party to determine and sign a strong reciprocity entanglement contract, both parties can ensure a complete quantum strategy to maximize cooperation and achieve Pareto optimality, ultimately enabling the long-term and stable development of the public goods industry project.