Co-evolution dynamics between individual strategy and gaming environment under the feedback control

Abstract

A co-evolution between individual strategy and gaming environment in two systems with two strategies 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. Besides, we employ two typical game models, prisoner’s dilemma game and division of labor game as two illustrative examples. In this framework, we derive the sufficient condition under feedback mechanism, under which the state of strategy and environment will evolve periodically. Results provide some inspirations to tackle with the cooperation dilemma and realize the effective division of labor in the real situations.