Research Papers

Evan Munro, PhD Student, Stanford University
Martino Banchio, PhD Student, Stanford University

Canonical tournament theory structures prizes that are decreasing in rank. In many practical settings, however, the lowest-ranked individuals receive a prize that is higher than middle-ranked individuals. In the major U.S. sports leagues, the most valuable new eligible players are allocated through a draft. To ensure long-term competitiveness of sports franchises, draft picks are allocated with a higher probability to the worst teams in a league. This causes some teams to exert less effort later in the season to secure a valuable draft pick with higher probability. We derive a theoretical model of team decision-making, and we prove that any lottery based on end of season rankings that does not treat all non-playoff teams equally will provide incentives for some teams to lose intentionally. We relax the constraint that the rule depends on the final rankings only, and design a lottery that eliminates tanking, favors the worst teams in a season and is optimal in a restricted class of mechanisms. We show the benefits of this new mechanism in simulations and empirically using data from the National Basketball Association.