Designing competitions between teams of individuals

Abstract

We consider a setting with two teams, each with a number of players. There is an ordering of all players that determines outcome of matches between any two players from the opposing teams. Neither the teams nor the competition designer know this ordering, but each team knows the derived ordering of strengths among its own players. Each team announces an ordering of its players, and the competition designer schedules matches according to the announced orderings. This setting in general allows for two types of manipulations by a team: Misreporting the strength ordering (lack of truthfulness), and deliberately losing a match (moral hazard). We prove necessary and sufficient conditions for a set of competition rules to have the properties that truthful reporting are dominant strategies and maximum effort in matches are Nash equilibrium strategies, and certain fairness conditions are met. Extensions of the original setting are discussed. © 2010 Elsevier B.V. All rights reserved.