Eco-evolutionary dynamics of bimatrix games

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