Minimax Play at Wimbledon Redux

Abstract

Initial tests of the predictive power of the mixed-strategy Nash equilibrium in the laboratory pointed to significant deviations. In response to the flat maximum critique, that incentives in the lab were not high enough to induce Nash behavior, researchers turned to the field, particularly sporting environments, where the monetary incentives were high. Field experiments overall, found predictions closer to the marginal distribution of actions predicted by the mixed strategy Nash equilibrium; however, evidence of deviations from the prediction of independent behavior across rounds have been mixed. I use a new dataset of tennis match serves that is two orders of magnitude greater than those used in previous tennis studies. Similarly to previous findings, the marginal distributions of professionals’ serves are not significantly different from the prediction of the normative solution, but there exists significant serial dependence across serves. This behavior is found even among players who at some point in their careers were ranked Number 1 in the world. The deviations of these top players cannot be explained as a strategic best response to expectations of lower-ranked players’ deviations from the Nash equilibrium.