John Rust, Georgetown University

"Disequilibrium Play in Tennis"

Abstract

Are the serves of the world’s best tennis pros consistent with the theoretical prediction of Nash equilibrium in mixed strategies? We analyze their serve direction choices (to the returner’s left, right or body) with data from an online database called the Match Charting Project. Using a new methodology, we test and decisively reject a key implication of a mixed strategy Nash equilibrium, namely, that the probability of winning a service game is the same for all serve directions. We also use dynamic programming (DP) to numerically solve for the best-response serve strategies to probability models of service game outcomes estimated for individual server-returner pairs, such as Novak Djokovic serving to Rafael Nadal. We show that for most elite pro servers, the DP serve strategy significantly increases their service game win probability compared to the mixed strategies they actually use, which we estimate using flexible reduced-form logit models. Stochastic simulations verify that our results are robust to estimation error.

Keywords: Tennis, games, Nash equilibrium, Minimax theorem, constant sum games, mixed strategies, dynamic directional games, binary Markov games, dynamic programming, structural estimation, muscle memory.

(Joint with: Axel Anderson, Georgetown University, Jeremy Rosen, Topspin Shot Research and Kin-Ping Wong, Digonex)

Contact person: Bertel Schjerning