When Are Mixed Equilibria Relevant?

44 Pages Posted: 5 Sep 2019 Last revised: 21 Dec 2020

See all articles by Daniel Friedman

Daniel Friedman

University of California, Santa Cruz - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Shuchen Zhao

University of California, Santa Cruz, Division of Social Sciences, Department of Economics, Students

Date Written: November 20, 2020

Abstract

Mixed Nash equilibrium (NE) is a cornerstone of game theory, but its empirical relevance has always been questionable. We study in the laboratory two games whose unique NE is in completely mixed strategies; other treatments include the matching protocol (pairwise random vs population mean matching), whether time is discrete or continuous, and whether players can specify mixtures explicitly or only pure strategy realizations. NE mixes predict observed behavior better than maximin in all treatments, but uniform mixes are better predictors than any equilibrium mixture in many treatments. By contrast, in a control game with a unique NE in pure strategies, the best point prediction is NE. Mixed equilibrium predictions are more useful in population mean matching than in standard pairwise matching. Regret-based sign preserving dynamics capture regularities across all treatments.

Keywords: Nash equilibrium, minimax, mixed strategy, directional learning, laboratory experiment

JEL Classification: C72, C73, C92

Suggested Citation

Friedman, Daniel and Zhao, Shuchen, When Are Mixed Equilibria Relevant? (November 20, 2020). Available at SSRN: https://ssrn.com/abstract=3444439 or http://dx.doi.org/10.2139/ssrn.3444439

Daniel Friedman (Contact Author)

University of California, Santa Cruz - Department of Economics ( email )

Social Sciences I
Santa Cruz, CA 95064
United States
831-459-4981 (Phone)
831-459-5900 (Fax)

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

Shuchen Zhao

University of California, Santa Cruz, Division of Social Sciences, Department of Economics, Students ( email )

CA
United States
2133599551 (Phone)

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