Evolutionary dynamics of N-person snowdrift game

• We construct a double-threshold model for multi-player snowdrift game.
• Fixation probability of cooperators presents characteristics of both coordination and coexistence games.
• The critical benefit-to-cost ratio that favors cooperation increases with average degree of the network.

In this letter, we investigate the evolutionary dynamics of N-person snowdrift game in both well-mixed and structured populations. For well-mixed populations, we construct a double-threshold model considering both the necessary and the minimum cost players should pay for completing the task. We have explored the influences of these thresholds on both equilibrium points in infinite populations and the fixation probabilities in finite populations. Results present complicated behaviors that show characteristics of both stag-hunt game and snowdrift game. For structured populations, we use pair approximation and diffusion approximation to derive the critical benefit-to-cost ratio in favor of cooperation.