Optimal prize design in team contests with pairwise battles

This paper studies the effort-maximizing design of a team contest with an arbitrary number (odd or even) of pairwise battles. In a setting with full heterogeneity across players and battles, the organizer determines the prize allocation rule (or the winning rule of an indivisible prize) contingent on battle outcomes. We propose a measure of team's strength, which plays a crucial role in prize design. The optimal design is a majority-score rule with a headstart score granted to the weaker team: All battles are assigned team-invariant scores, the weaker team is given an initial headstart score which is the difference in strengths between teams, and the team collecting higher total scores from its winning battles wins the entire prize. The optimal rule resembles the widely-adopted Elo rating system.