Endogenous Feedback in Coevolutionary Games Reshapes the Stability of Cooperation

TL;DR

This paper introduces an endogenous-feedback model in coevolutionary games, showing how collective behavior influences payoffs, leading to new regimes like chimera games and complex stability dynamics.

Contribution

It presents a novel endogenous-feedback framework where payoffs depend on cooperation levels, revealing feedback-induced regimes and stability phenomena not seen in fixed-game models.

Findings

Feedback can promote stable cooperation in chimera games.

Delayed feedback can destabilize equilibria and cause oscillations.

Nonlinear feedback introduces path dependence and reshapes equilibrium structure.

Abstract

In Evolutionary game theory the payoffs are typically fixed or shaped by external environmental variables. Here, we introduce an endogenous-feedback model in which the game played coevolves directly with the population state: the payoff matrix is a time-dependent function of the level of cooperation. This allows strategic incentives to be continuously modified by the collective behavior they generate. Even in the simplest case of linear and instantaneous feedback, the model reveals feedback-induced regimes, termed chimera games, in which stable cooperation arises despite being incompatible with the predictions of standard fixed-game dynamics. We further show that delayed feedback can destabilize these equilibria and generate sustained oscillations, while nonlinear feedback reshapes equilibrium structure and introduces path dependence. Our results show how cooperation can be promoted, suppressed, or destabilized by incentives generated endogenously by the very same population's collective behavior. We conclude by outlining how our framework connects to real-world systems shaped by endogenous feedback.