A Graph-Theoretic Analysis of Distributed Replicator Dynamic

TL;DR

This paper introduces a graph-theoretic approach to analyze population dynamics in multi-agent systems, focusing on stability and truncation behavior using spectral properties of the graph Laplacian.

Contribution

It develops a novel graph-theoretic framework linking population fitness dynamics to graph spectral properties, enhancing understanding of stability and truncation in population games.

Findings

Spectral properties of the Laplacian relate to stability of population dynamics.

Fitness agreement protocol ensures asymptotic stability.

Simulation results support the theoretical analysis.

Abstract

This paper attempts to develop a graph-theoretic multi-agent perspective of population games to study the \quotes{truncation} behavior. The proposed method considers fitness of the population as a dynamical system to address the issue of restrictive description of this behavior which pertains to the underlying population dynamic. The fitness dynamic resembles an agreement protocol that enables comments on the steady-state characteristics of the graph that represents the population structure. The structural attributes of the underlying graph and the truncation behavior are emphasized by exploiting the spectral properties of the associated Laplacian matrix. The asymptotic stability of the fitness agreement protocol has been shown to be sufficient in concluding the stability of population dynamics. Simulation results validating the proposed hypothesis have been discussed.