The Gender Difference in Mixed Strategy Nash Equilibrium Play

Abstract

The mixed strategy Nash equilibrium (MNE) is a well-established concept in theory, but empirical and experimental support has been hampered by the need for a large sample size for across-subject choices and serial correlation for within-subject choices. We overcome these difficulties in testing for MNE play by exploiting a previously developed comparative statics effect for a common value pairwise all-pay auction which, strikingly, predicts that bids increase on perceived opponent’s risk tolerance, but not on the bidder’s own. Men bid as predicted, but women’s bids respond neither to their own nor to the opponent’s risk tolerance. Additionally, while the significance of men’s response to their beliefs about their opponent’s risk tolerance increases with the absence of mistakes on a pre-experiment quiz, women’s lack of response is unaffected by their quiz performance. These results are consistent with a prior finding of a gender difference in MNE play with a large sample of professional tennis players. We contribute by showing that MNE play can be tested with an ordinary sample of subjects in a laboratory setting. We show a gender difference in a factor that is likely crucial in most competitive situations: perceptions of the opponent’s risk tolerance.