Coevolutionary dynamics of feedback-evolving games in structured populations

TL;DR

This paper explores how population structure influences the coevolution of strategies and environmental states in feedback-evolving games, revealing diverse dynamics like oscillation, bistability, and coexistence through theoretical and simulation analyses.

Contribution

It introduces a coevolution model on structured populations and demonstrates how neighborhood size affects environmental and strategic dynamics, extending feedback-evolving game theory.

Findings

Different evolutionary outcomes including oscillation, bistability, and coexistence.

Neighborhood size influences the stability and size of basins of attraction.

Environmental and strategic dynamics depend on local interactions and payoff ratios.

Abstract

The interdependence between an individual strategy decision and the resulting change of environmental state is often a subtle process. Feedback-evolving games have been a prevalent framework for studying such feedback in well-mixed populations, yielding important insights into the coevolutionary dynamics. However, since real populations are usually structured, it is essential to explore how population structure affects such coevolutionary dynamics. Our work proposes a coevolution model of strategies and environmental state in a structured population depicted by a regular graph. We investigate the system dynamics, and theoretically demonstrate that there exist different evolutionary outcomes including oscillation, bistability, the coexistence of oscillation and dominance, as well as the coexistence of cooperation and defection. Our theoretical predictions are validated through numerical calculations. By using Monte Carlo simulations we examine how the number of neighbors influences the coevolutionary dynamics, particularly the size of the attractive domain of the replete environmental state in the cases of bistability or cooperation-defection coexistence. Specifically, in the case of bistability, a larger neighborhood size may be beneficial to save the environment when the environmental enhancement rate by cooperation / degradation rate by defection is high. Conversely, if this ratio is low, a smaller neighborhood size is more beneficial. In the case of cooperator-defector coexistence, environmental maintenance is basically influenced by individual payoffs. When the ratio of temptation minus reward versus punishment minus sucker's payoff is high, a larger neighborhood size is more favorable. In contrast, when the mentioned ratio is low, a smaller neighborhood size is more advantageous.