Ex post unbalanced tournaments

Tournaments create strong incentives under the assumption that the competition between the agents is balanced. If, at the outset, one agent is stronger than the other, the tournament is ex ante unbalanced and incentives break down. Handicaps can in this case restore incentives. In practice, competing agents are often overall equally strong but have different sorts of strengths. Then, competition will typically be unbalanced ex post and incentives break down, but handicaps cannot be used. We show how a simple means, introducing the possibility of a tie, can often resolve the problem. We examine under what conditions incentives are maximized by ties.