The paper addresses the problem of optimally matching heterogeneous players in a two-stage two-type Lazear-Rosen tournament in which the semifinal losers are eliminated. The organizer of the tournament can either choose two homogeneous semifinals -- one between two strong players and the other one between two weak players -- or two heterogeneous semifinals, each between one strong and one weak player. I identify conditions under which the organizer is strictly better off from two homogeneous semifinals if he wants to maximize total expected effort and the strong players' win probability. This finding is contrary to both the typical procedure used in real sporting contests and previous results based on all-pay auctions and the Tullock contest. Hence, my findings point out that the optimal design of elimination tournaments crucially depends on the underlying contest-success technology.
Lazear-Rosen tournament heterogeneous match homogeneous match