Replicator equation on networks with degree regular communities

TL;DR

This paper extends the replicator equation to degree-regular community networks, analyzing how network structure influences evolutionary game equilibria.

Contribution

It introduces a replicator equation tailored for networks with degree-regular communities, advancing the understanding of evolutionary dynamics on complex networks.

Findings

Network structure affects equilibrium outcomes in evolutionary games.

Degree-regular community networks can be modeled with a specialized replicator equation.

The approach reveals how community topology influences evolutionary stability.

Abstract

The replicator equation is one of the fundamental tools to study evolutionary dynamics in well-mixed populations. This paper contributes to the literature on evolutionary graph theory, providing a version of the replicator equation for a family of connected networks with communities, where nodes in the same community have the same degree. This replicator equation is applied to the study of different classes of games, exploring the impact of the graph structure on the equilibria of the evolutionary dynamics.