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.