A Stochastic Stability Analysis with Observation Errors in Normal Form Games

34 Pages Posted: 16 Apr 2019 Last revised: 14 Nov 2019

Date Written: February 15, 2019

Abstract

We perform a stochastic stability analysis with observation errors. Players recurrently play a symmetric two-player normal form game with one another and respond to the strategy distribution of other players. In each period, a revising player observes the strategy distribution and choose a best response to it. Her observation is perturbed with positive probability and she may respond to the misperceived strategy distribution. We examine the robustness of Nash equilibria to such observation errors. We find that the set of stochastically stable states under observation errors is robust to addition of strictly dominated strategies for a certain class of games given that observation errors are uniform, i.e., each misrepresented state is observed with uniform probability. We also examine the set of stochastically stable states under an alternate observation error model where the observation probability depends on the L1-norm between the true state and the observed state. For the local interaction model, we prove that the set of stochastically stable states under both observation error models is robust to addition of strategies that do not survive the iterative elimination of strictly dominated strategies provided that the population size is sufficiently large.

Keywords: Stochastic stability, Observation errors, Action errors, Local interactions

JEL Classification: C72, C73

Suggested Citation

Sawa, Ryoji, A Stochastic Stability Analysis with Observation Errors in Normal Form Games (February 15, 2019). Available at SSRN: https://ssrn.com/abstract=3362200 or http://dx.doi.org/10.2139/ssrn.3362200

Ryoji Sawa (Contact Author)

University of Tsukuba ( email )

Japan

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