Coupled replicator equations for the dynamics of learning in multiagent systems

2002/04/30 by Yuzuru Sato, James P. Crutchfield · 4 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Nonlinear Dynamics and Pattern Formation #nlin.AO #nlin.CD

paper · pdf · doi:10.1103/physreve.67.015206

4 pages, 3 figures, http://www.santafe.edu/projects/CompMech/papers/credlmas.html; updated references, corrected typos, changed content

arxiv created 2002/08/18 · openalex publication_date 2003/01/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Starting with a group of reinforcement-learning agents we derive coupled replicator equations that describe the dynamics of collective learning in multiagent systems. We show that, although agents model their environment in a self-interested way without sharing knowledge, a game dynamics emerges naturally through environment-mediated interactions. An application to rock-scissors-paper game interactions shows that the collective learning dynamics exhibits a diversity of competitive and cooperative behaviors. These include quasiperiodicity, stable limit cycles, intermittency, and deterministic chaos-behaviors that should be expected in heterogeneous multiagent systems described by the general replicator equations we derive.

Citations

• Evolutionary stable strategies and game dynamics
• Construction of higher order symplectic integrators
• Reinforcement Learning: An Introduction

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