Cooperation in Public Goods Games over Uniform Random Hypergraphs with Game Transitions

The evolution of cooperation is a central enigma in evolutionary game theory. Traditionally, the combination of pairwise networks and repeated Public Goods Games with a single state fails to adequately describe realistic group interaction scenarios. On the one hand, pairwise networks lack clear group definitions. On the other hand, a participant's decision affects not only competitors' fitness but also the state of the surrounding environment. To address this problem, we propose a Public Goods Game with game transition mechanisms based on Uniform Random Hypergraphs. In our model, game groups formed by hyperedges transition between two types of games, one with abundant public resources and the other with scarce public resources. The transition probability is closely related to the strategies of players within the hyperedges. By developing a Monte Carlo simulation framework that incorporates payoff accumulation, strategy imitation, and game state transitions, we aim to reveal the coevolutionary patterns of strategies and game states in group interactions. Our study highlights a nonlinear relationship between defection sensitivity and cooperation frequency under game transitions, as well as the asymmetric effects of the two sensitivities in state-dependent transitions. These observations open new directions for how to approach social dilemmas.