Evolutionary dynamics of individual strategies and game environments in the framework of feedback control

A model of co-evolution between individual strategy and gaming environment is proposed here. Different from the general evolutionary game dynamics, the gaming system developed here is deeply coupled with the strategy choices and the environment state. The game state, payoff matrices and gaming environment of the system will influence each other dynamically. We firstly analyse the co-evolution between two populations with two strategies and derive the sufficient condition under which the state of strategy and environment will evolve periodically. Then we extend the model to multiple populations and strategies to study a more complicated and realistic system. In this framework, we verify whether and how the convergence will take place among groups in the multi-strategy case. Our results provide some inspirations to tackle with the cooperation dilemma and research on the self-organized evolution in multi-behaviour populations in the real-world situations.