  Feedbacks between strategies and the environment are common in
social-ecological, evolutionary-ecological, and even psychological-economic
systems. Utilizing common resources is always a dilemma for community members,
like tragedy of the commons. Here we consider replicator dynamics with
feedback-evolving games, where the payoffs switch between two different
matrices. Although each payoff matrix on its own represents an environment
where cooperators and defectors can't coexist stably, we show that it's
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.
