Designing fair tiebreak mechanisms for sequential team contests

Abstract

Economists have long recognized that the effect of the order of actions in sequential contests on performance of the contestants is far from negligible. We model the tiebreak mechanisms, known as penalty shootouts, which have sequential move order and are used in several team-sports contests, as a dynamic mechanism-design problem with a fairness desideratum in mind. In most sports, such as soccer and hockey, the order in which teams take the penalties is fixed, known as ABAB. We first show that even with two balanced teams, this mechanism possesses many symmetric Markov-perfect equilibria giving various asymmetric winning probabilities to the first- and second-moving teams (but favoring the first mover under appropriate refinements) –– an observation which also obtained some empirical support for soccer. Following that, we characterize all sequentially fair mechanisms in which two balanced teams have equal chances to win the shootout whenever the score is tied after equal numbers of attempts. Using additional desirable properties, we uniquely characterize practical mechanisms for easy and difficult shootouts, in which the success probability of a penalty kick is uniformly greater than 50% or less than 50%, as in soccer and hockey, respectively.