The distribution of wealth and the effect of extortion in structured populations

Despite that the heterogeneous distribution of wealth is widely observed in social, economical and biological system, few studies have been conducted to explore its influence on the evolutionary dynamics in populations. This paper discusses this problem by introducing a heterogeneous wealth allocation mechanism controlled by a tunable parameterα . Our study shows that there is a positive relationship between the level of cooperation and the extent of heterogeneity of wealth distribution. More importantly, we show that the catalytic effect of extortioners can be significantly strengthened if wealth is heterogeneously distributed among the whole population. Cooperators and extortioners can co-exist if the value of αis moderate. We explain this phenomenon by arguing that this heterogeneous allocation mechanism enables three types of strategists to form clusters around several rich cooperating neighbors initially. Clusters of defectors tend to be eliminated at early stages of evolution.