Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics

William H. Sandholm, Mathias Staudigl

Research output: Contribution to journalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)1348-1377
Number of pages30
JournalMathematics of Operations Research
Volume43
Issue number4
Early online date27 Jul 2018
DOIs
Publication statusPublished - Nov 2018

Keywords

  • sample path large deviations
  • evolutionary game theory
  • stochastic stability
  • Markov chains
  • potential games
  • congestion games
  • STATIONARY DISTRIBUTIONS
  • DIFFERENTIAL-EQUATIONS
  • RECURSIVE ALGORITHMS
  • LONG-RUN
  • STABILITY
  • EQUILIBRIA
  • LIMITS

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