Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics

TL;DR

This paper establishes a large deviation principle for stochastic evolutionary game dynamics, providing insights into the probabilities of atypical paths and their asymptotic behaviors as population size grows.

Contribution

It introduces a rigorous large deviation framework for stochastic evolutionary games, including explicit calculations for logit choice in potential games.

Findings

Derived a sample path large deviation principle for the model

Characterized excursion rates and stationary distribution asymptotics

Explicitly computed rates for logit choice in potential games

Abstract

We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of decay of the probability that the sample path of the evolutionary process lies in a prespecified set as the population size approaches infinity. We use these results to describe excursion rates and stationary distribution asymptotics in settings where the mean dynamic admits a globally attracting state, and we compute these rates explicitly for the case of logit choice in potential games.