Evolutionary Game Dynamics for Two Interacting Populations under Environmental Feedback

TL;DR

This paper models the co-evolution of two populations' strategies and environmental states using replicator dynamics, revealing conditions for convergence and oscillations in societal feedback systems.

Contribution

It introduces a framework for analyzing joint evolution of payoffs and environment, highlighting oscillatory behaviors and convergence conditions in multi-population dynamics.

Findings

Identification of scenarios with stable convergence

Conditions leading to oscillatory dynamics

Application to societal evolution models

Abstract

We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the environment: the payoff matrix varies with the changing environment and at the same time, the state of the environment is affected indirectly by the changing payoff matrix through the evolving population profiles. For such co-evolutionary dynamics, we investigate whether convergence will take place, and if so, how. In particular, we identify the scenarios where oscillation offers the best predictions of long-run behavior by using reversible system theory. The obtained results are useful to describe the evolution of multi-community societies in which individuals' payoffs and societal feedback interact.