by Joel Wiles

Abstract 

A mixed strategy is a random choice among available strategies, with each strategy being chosen a set percentage of the time. In many games that require unpredictable play, game theory predicts that a mixed strategy equilibrium, a situation where each player uses an optimal mixed strategy, will result. Economists have tested whether people play according to the mixed strategy equilibrium in laboratory experiments with two player zero-sum games—subjects in these experiments generally do not play in accordance with game theory’s predictions. Recently, economists have published papers examining mixed strategy equilibrium play using professional sports as a natural experiment. This paper builds upon Walker and Wooders (2001), which examines mixed strategy play in the locations of serves in professional tennis matches. Walker and Wooders (2001) find that professional tennis players are closer to game theory’s predictions than subjects in laboratory settings, but still “switch their serves up” more than is consistent with game theory’s predictions. My hypothesis is that this result can be explained by a short-term timing effect where a serve that has just been hit is, ceteris paribus, less effective on the next point. I construct a model incorporating this timing effect and work out the theoretical implications of my model. I then estimate the magnitude of this timing effect and determine if optimal play under this model is consistent with the results obtained by Walker and Wooders. My conclusion is that the model accounts for a little under half of the deviation from game theory’s predictions found in the data from professional tennis matches. This suggests that professional tennis players play closer to game theory’s predictions when tested using a model designed to account for more of the complexities of tennis than the Walker and Wooders model, but they still do not play in complete accordance with those predictions.

Professor Curtis Taylor, Faculty Advisor

JEL Codes: Z20,

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