Eco-Evolutionary Dynamics of Bimatrix Games

TL;DR

This paper explores how feedback mechanisms in eco-evolutionary games can lead to persistent oscillations in strategies, offering insights into controlling population states in social and biological systems.

Contribution

It introduces a novel framework of replicator dynamics with switching payoff matrices, demonstrating the possibility of sustained strategy oscillations through control laws.

Findings

Switching payoff matrices can induce stable strategy oscillations.

Designing control laws enables persistent eco-evolutionary dynamics.

Applicable to microbial experiments and social-ecological systems.

Abstract

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.