Designing Practical and Fair Sequential Team Contests

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 practical dynamic mechanism-design problem. We characterize all order-independent mechanisms; in such mechanisms two balanced teams have equal chances to win the shootout whenever the score is tied after equal numbers of attempts and hence move order has no relevance for winning chances. Using additional desirable properties, we uniquely characterize practical mechanisms. In most sports, such as football and hockey, the order in which teams take the penalties is fixed, known as ABAB, and a few high-level football competitions recently adopted the alternating-order variant mechanism, ABBA. Our results imply that these two and all other exogenous-order mechanisms – with one exception – are order dependent in regular rounds. Although ABBA is order independent in sudden-death rounds, ABAB fails there, too. Our theory supports empirical studies linking ABAB to unfair outcomes and multiple equilibria in terms of winning chances of the first- vs. second-kicking teams in different football traditions.