Stochastic stability in the large population and small mutation limits for coordination games

Ryoji Sawa

doi:10.3934/jdg.2021015

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2022, Volume 9, Issue 4: 547-567. Doi: 10.3934/jdg.2021015

This issue Previous Article Stochastic dynamics and Edmonds' algorithm Next Article Large deviations and Stochastic stability in Population Games

Stochastic stability in the large population and small mutation limits for coordination games

Ryoji Sawa^*,

University of Tsukuba, Tennoudai 1-1-1, Tsukuba, Ibaraki 305-8573, Japan

^* I dedicate this paper to William H. Sandholm.

Received: October 2020

Early access: April 2021

Published: October 2022

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Abstract

We consider a model of stochastic evolution in symmetric coordination games with $ K\ge 2 $ strategies played by myopic agents. Agents employ the best response with mutations choice rule and simultaneously revise strategies in each period. We form the dynamic process as a Markov chain with state space being the set of best responses in order to overcome difficulties that arise with the large population. We examine the long run equilibria for both orders of limits where the small noise limit and the large population limit are taken sequentially. We characterize an equilibrium refinement criterion that is common among both orders of limits.

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Mathematics Subject Classification: Primary: 91A22, 60F10, 60J10; Secondary: 91A11, 91D15.

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Figure 1. The literature on stochastic stability in the large population limit

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