Eco-evolutionary dynamics of bimatrix games

Feedbacks between strategies and the environment are common in social-ecological, evolutionary-ecological, even psychological-economic systems. Utilizing resources is always a dilemma for community members, like tragedy of commons. Here we consider replicator dynamics with feedback-evolving games, where payoffs switch two different matrices. Although each payoff matrix on its own represents an cooperators defectors can't coexist stably, show that it's possible to design appropriate switching control laws achieve persistent oscillations strategy abundance. This result should help guide widespread problem population state microbial experiments other social problems eco-evolutionary feedback loops.