# American Institute of Mathematical Sciences

doi: 10.3934/jdg.2021015

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

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

* I dedicate this paper to William H. Sandholm.

Received  October 2020 Published  April 2021

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.

Citation: Ryoji Sawa. Stochastic stability in the large population and small mutation limits for coordination games. Journal of Dynamics & Games, doi: 10.3934/jdg.2021015
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