Co-evolution of limited resources in the memory-based spatial evolutionary game

In this paper, the co-evolution of cooperation and limited resources in spatial evolutionary game is studied, where memory ability is involved in the evolutionary process. Competition for resources exists widely in nature and human society. Therefore, the allocation of limited resources is always accompanied with various kinds of games. The acquisition of resources depends on the results of the game and the number of resources owned by the players would in turn affect the choice of game strategies. Memory, or so-called experience, usually plays an important role in guiding human behaviors in the real world, which is vital to individual rational decision-making. In order to better simulate the memory ability in real life, memory mechanism with attenuation factor is introduced into the co-evolution of prisoner's dilemma game. Moreover, in order to protect the vulnerable groups, we have introduced the mechanism of minimum guarantee of resources, which simulates the social security system in reality such that the extreme polarization can be alleviated. By using strategy-independent rules, memory ability can effectively raise the level of cooperation, where both the memory length and attenuation factor would affect the co-evolutionary results. Furthermore, limited resources have fast aggregation effect and players with cooperative behaviors have easier access to resources. Meanwhile, the minimum resources guarantee mechanism can considerably affect the cooperation level. Besides, as to the complex dynamical behaviors of co-evolution, quantitative and qualitative discussions are implemented. In order to illustrate the robustness of the obtained results, the cooperative behaviors of systems in public goods game and snow game are also discussed.