On stochastic imitation dynamics in large-scale networks

TL;DR

This paper analyzes stochastic imitation dynamics in large networks, showing convergence and stability near equilibrium strategies, and extends results to complex network interactions beyond complete graphs.

Contribution

It introduces a broad class of stochastic imitation models, proving convergence and stability results, and extends analysis to complex network structures.

Findings

Convergence to stable strategies in potential population games.

Meta-stability phenomena in stochastic imitation dynamics.

Extension of results to complex network interactions.

Abstract

We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game structure: they only know their own current utility and the one of neighbor players contacted through pairwise interactions in a network. In response to this information, players update their state according to some stochastic rules. For potential population games and complete interaction networks, we prove convergence and long-lasting permanence close to the evolutionary stable strategies of the game. These results refine and extend the ones known for deterministic imitation dynamics as they account for new emerging behaviors including meta-stability of the equilibria. Finally, we discuss extensions of our results beyond the fully mixed case, studying imitation dynamics where agents interact on complex communication networks.