Bargaining-based cost sharing shapes the evolution of cooperation in snowdrift games

Cost sharing in the snowdrift game is usually determined only by the strategies of interacting individuals. However, in many collective tasks, the division of cost also depends on whether the participants can reach an acceptable agreement. We, therefore, propose a bargaining-based snowdrift game in which each individual has a bargaining parameter describing the fraction of the cost that the individual would prefer the other participant to bear. In a cooperator-defector interaction, the cost is shared only when their bargaining preferences are compatible; otherwise, the cooperator bears the full cost. We derive a mean-field replicator equation with strategy mutation and examine the model through numerical simulations in well-mixed and networked populations. The results show that cooperation decreases as the cost increases. Distributions concentrated at lower bargaining parameters promote cooperation by increasing the probability of successful cost sharing and reducing the payoff disadvantage of cooperators. Distributions with the same mean can produce different cooperation levels, indicating that the shape of the bargaining-parameter distribution is important. Weak mutation has little effect on the ordering among distributions, whereas strong mutation reduces their differences. Increasing network connectivity generally promotes the cooperation, and the effect of bargaining heterogeneity remains consistent across different network structures. These results show that negotiated cost sharing can influence the evolution of cooperation.