How do People Play Against Nash Opponents?

28 Pages Posted: 6 Apr 2011  

Jason Shachat

WISE Xiamen University

J. Todd Swarthout

Georgia State University - Andrew Young School of Policy Studies

Lijia Wei

Wuhan University - School of Economics and Management; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE)

Date Written: February 21, 2011

Abstract

We examine experimentally how humans behave when they play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects' play was consistent with their Nash equilibrium strategy, while a larger percentage of subjects' play was more consistent with different models of play: equiprobable play for the zero-sum game, and the minimax strategy in the unprofitable game. We estimate the heterogeneity and dynamics of the subjects' latent mixed strategy sequences via a hidden Markov model. This provides clear results on the identification of the use of pure and mixed strategies and the limiting distribution over strategies. The mixed strategy Nash equilibrium is not self-enforcing except when it coincides with the equal probability mixed strategy, and there is surprising amounts of pure strategy play and clear cycling between the pure strategy states.

Keywords: Mixed Strategy, Nash Equilibrium, Experiment, Hidden Markov Model

JEL Classification: C92, C72, C10

Suggested Citation

Shachat, Jason and Swarthout, J. Todd and Wei, Lijia, How do People Play Against Nash Opponents? (February 21, 2011). Available at SSRN: https://ssrn.com/abstract=1803430 or http://dx.doi.org/10.2139/ssrn.1803430

Jason Shachat (Contact Author)

WISE Xiamen University ( email )

A 307, Economics Building
Xiamen, Fujian 361005
China

J. Todd Swarthout

Georgia State University - Andrew Young School of Policy Studies ( email )

P.O. Box 3992
Atlanta, GA 30302-3992
United States

Lijia Wei

Wuhan University - School of Economics and Management ( email )

Wu Han, Hu-Bai 430072
China

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 361005
China

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