Evolutionary dynamics of multi-player snowdrift games based on the Wright-Fisher process

Although cooperative behavior is ubiquitous in biological and social systems, the causes and mechanisms of cooperation are a basic problem in evolutionary theory. The snowdrift game is considered as an effective evolutionary game model to describe cooperative behavior in a competitive situation. Thus, this paper studies the evolutionary dynamics of cooperative behavior in multi-player snowdrift games. This work establishes a stochastic two-strategy multi-player snowdrift game based on the Wright-Fisher (W-F) update process. Next, a specific analytical expression for fixation probabilities of cooperation and defection is considered, and the conditions under which cooperative strategies take root in a population and become an evolutionarily stable strategy are given. Finally, the relationships between the fixation probability of cooperation and each parameter involved in the game are obtained via simulation analysis. A simulation analysis reveals that the fixation probability of cooperation decreases with selection intensity, the number of players playing in multi-player snowdrift games, and population size but increases with the benefit-cost ratio. The present work promotes an understanding of the evolutionary dynamics of cooperative behavior and the theory of multi-player snowdrift games with the W-F update process.