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Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics

Author

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  • William H. Sandholm

    (Department of Economics, University of Wisconsin–Madison, Madison, Wisconsin 53706)

  • Mathias Staudigl

    (Department of Quantitative Economics, Maastricht University, NL-6200 MD Maastricht, Netherlands)

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.

Suggested Citation

  • William H. Sandholm & Mathias Staudigl, 2018. "Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1348-1377, November.
    • Handle: RePEc:inm:ormoor:v:43:y:2018:i:4:p:1348-1377
    DOI: 10.1287/moor.2017.0908
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    References listed on IDEAS

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    Cited by:

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