Promotion of cooperation induced by heterogeneity of both investment and payoff allocation in spatial public goods game

Heterogeneity has attracted mounting attention across multiple disciplines and is confirmed to be a greater promoter of cooperation. It is often the case that the heterogeneity always exists in investment and payoff allocation concurrently instead of separately. In addition, the factors that affect heterogeneous investment and payoff allocation are various. Inspired by this, this paper extends the previous models by incorporating heterogeneous investment and payoff allocation into the typical PGG model to further investigate the incentive mechanisms of cooperative behavior. In order to better understand the model, three different feedback mechanisms, namely the wealth-preference mechanism, the social-self-preference mechanism, and the mixed-preference mechanism, are addressed. The former two mechanisms correspond to the case of single factor and the latter corresponds to the case of double factors. The numerical simulations indicate that feedback mechanism by bridging the connections between the investment and the payoff allocation can reduce the free-rider problem. Furthermore, it is found that the cooperative frequency and average payoff perform better in the case of the mixed-preference mechanism where players will not only take previous payoff feedback as well as current investment but also their social status into their game decision-making process. In addition, full cooperation and profitability over all players can be promoted by means of increasing r or reducing α. At last, compared with another two classic networks, the extent of cooperation is promoted under the structures of the BA scale free networks.