Replicator Dynamics of Co-Evolving Networks

TL;DR

This paper introduces a model where agents in a network adapt their strategies and connections through reinforcement learning, with the system's evolution described by replicator dynamics equations, illustrating co-evolution of strategies and network structure.

Contribution

It presents a novel framework combining game theory, reinforcement learning, and network co-evolution through replicator dynamics equations.

Findings

The model captures the joint evolution of strategies and network links.

Replicator dynamics effectively describe the co-evolution process.

Illustrative examples demonstrate the framework's applicability.

Abstract

We propose a simple model of network co-evolution in a game-dynamical system of interacting agents that play repeated games with their neighbors, and adapt their behaviors and network links based on the outcome of those games. The adaptation is achieved through a simple reinforcement learning scheme. We show that the collective evolution of such a system can be described by appropriately defined replicator dynamics equations. In particular, we suggest an appropriate factorization of the agents' strategies that results in a coupled system of equations characterizing the evolution of both strategies and network structure, and illustrate the framework on two simple examples.