On stochastic imitation dynamics in large-scale networks
For researchers studying learning in games, this provides rigorous convergence guarantees for stochastic imitation dynamics, refining deterministic results and accounting for new behaviors like meta-stability.
The paper proves convergence and long-lasting permanence near evolutionary stable strategies for stochastic imitation dynamics in potential population games with complete networks, and extends results to complex networks, revealing meta-stability of equilibria.
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.