Asymmetric cost in snowdrift game on scale-free networks

We study the effects of asymmetric cost on the cooperative behavior in the snowdrift game on scale-free networks. The asymmetric cost reflects the inequality in mutual cooperation and the diversity of cooperators. We focus on the evolution of cooperation and the inequality in wealth distribution influenced by the degree of asymmetry in cost, related with cooperators' connections. Interestingly, we find that when cooperators with more neighbors have the advantage, cooperative behavior is highly promoted and the rich exploits the poor to get richer; while if cooperators with less neighbors are favored, cooperation is highly restricted and the rich are forced to offer some payoff to the poor so that the wealth is more homogeneously distributed. The wealth distribution in population is investigated by using the Gini coefficient and the Pareto exponent. Analytical results and discussions are provided to better explain our findings. The asymmetric cost enhances the leader effects in the decision making process by heterogeneous wealth distribution, leading not only to very high cooperator density but also to very stable cooperative behavior.