The Evolution of Submissive Clusters in the Spatial Snowdrift Game

The zero-determinant strategies can make an individual unilaterally enforce a linear relationship with her and coplayer’s payoffs. Traditionally, researchers focus on the evolution of zero-determinant strategies based on the Prisoner’s dilemma game. In this paper, in terms to the famous snowdrift game, we investigate the zero-determinant strategies in the regular graph. The spatial structure can hinder the spread of cooperative strategy in snowdrift game. The submissive strategy is a subset of zero-determinant strategies, which can provide less benefit to defectors than that of cooperative strategy. We find that the spatial structure can promote the emergence of submissive strategy although the payoff relationship between submissive strategy and defective strategy is also snowdrift-like. Moreover, from the perspective of formation pattern, we analyze the underlying mechanism about the evolution of zero-determinant strategies in the regular graph, which may provide some clues to understand cooperative dynamics and design protocols in the networked multi-agent systems.