DP8021 Round-Robin Tournaments with Effort Constraints

Author(s): Eyal Erez, Aner Sela
Publication Date: September 2010
Keyword(s): effort Constraints, Round-Robin Tournaments, Tullock Contests
JEL(s): D44
Programme Areas: Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=8021

We study a round-robin tournament with n symmetric players where in each of the n-1 stages each of the players competes against a different player in the Tullock contest. Each player has a limited budget of effort that decreases within the stages proportionally to the effort he exerted in the previous stages. We show that when the prize for winning (value of winning) is equal between the stages, a player's effort is weakly decreasing over the stages. We also show how the contest designer can influence the players' allocation of effort by changing the distribution of prizes between the stages. In particular, we analyze the optimal distribution of prizes over the stages that balance the effort allocation such that a player exerts the same effort over the different stages. In addition, we analyze the distribution of prizes over the stages that maximizes the players' expected total effort.