Co-evolution of cooperation and extortion with resource allocation in spatial multigame

In nature and human society, some agents want to obtain more payoffs by controlling own and opponents' strategy. The extortion strategy can unilaterally ensure that its own payoffs are not lower than its opponents', which has aroused widespread concern. In this article, based on spatial multigame, an evolutionary dynamics model with extortion strategy is proposed, which can significantly influence the evolution of different dilemma strategies in the system. Moreover, the limited resources as a co-evolutionary factor are also involved in this model. Throughout the entire evolutionary process, individuals in SDG and collaborators are more likely to obtain more resources and the number of resources owned by individuals in PDG is continuously decreasing. By using single square lattice network, we discuss in detail the evolutionary dynamics of the proposed model and study the impact of the sucker's payoff θ and extortion factor λ on different strategies of the system. Through a large number of experiments, it is found that the θ can significantly increase the number of cooperators. And there is an appropriate λ value, which can not increase the number of its own individuals, but also form an alliance with cooperators to jointly resist the intrusion of defectors. Besides, the relationship between θ, λ and network reciprocity is studied. We obtain that the θ and λ can significantly improve network reciprocity. Finally, based on different extortion factor λ, the proportion of different strategy in PDG and SDG is discussed to explain the robustness of the results.