The Distribution of Prizes in a Match-Play Tournament with Single Eliminations

Abstract

This paper begins to study the reward-incentive structure in sequential knock-out or elimination tournaments with matched, pairwise comparisons among players at each stage. The prize structure required to elicit constant expected quality of play in all matches throughout the tournament is characterized for competition among equally talented (or perfectly handicapped), players.The incentive maintaining prize structure is shown to concentrate' extra weight on the top ranking prize, a phenomenon observed in most tournaments. More can be said. Prizes that maintain performance incentives at all stages award a constant increment for each match won up to the last stage; and an amount greater than this for the player who wins the final match. Players' incentives to perform in early rounds are propelled by the probability of achieving higher ranks and surviving to later stages where rewards are larger. These continuation options are played out in the final match, so it is only the difference between winning and losing prizes in the finals that controls incentives there. Many athletic tournaments are structured in the manner analyzed here,but the general framework ultimately may have application to certain career games as well. More generally, a tournament structure may he viewed as a statistical, experimental design problem.The prize structure interacts with the design in providing incentives for the best players to survive to the finals and win the top prizes.