When Are Mixed Equilibria Relevant?

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, Maximin, Mixed strategy, Sign preserving dynamics, Laboratory experiment.

JEL Classification: C72, C73, C92