Evolutionary dynamics of multiplayer public goods game with the Wright-Fisher process

A public goods game (PGG) is a classical evolutionary dynamic model frequently used to explore group interaction and is widely used to explain the emergence and maintenance of cooperation among selfish individuals. This work attempts to study the dynamics of cooperation in a multiplayer PGG that is based on the Wright-Fisher process (WFP). Firstly, a general game -- multiplayer with two-strategy model based on the WFP -- is established to solve the fixation probability of the strategy and to give its natural properties. Then, the multiplayer PGG model with cooperation and defection strategies, based on the WFP, is established, and the fixation probabilities of strategies are solved. In addition, the natural properties of fixation probability are obtained, and the effect of game parameters on the evolution dynamics of cooperation strategy is received. The results show that a turning point of the return coefficient does exist. When the interest factor is greater than the turning point, the cooperative strategy is more likely to occupy the entire population and is an evolutionarily stable strategy (ESSN); the fixation probability of the cooperative strategy also increases in line with the increases in cost and choice intensity. Moreover, the fixation probability of the cooperative strategy increases in line with the increase in the interest factor, and decreases in line with the increase in the number of individuals playing the game and population size. The research in this paper will provide more insights into the evolution of cooperation in a multiplayer PGG.