Working Paper: CEPR ID: DP8021
Abstract: 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.
Keywords: effort constraints; roundrobin tournaments; tullock contests
JEL Codes: D44
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| prize distribution (D44) | players' effort allocation (D29) |
| identical prizes for all stages except the last one (D44) | players' effort allocation (D29) |
| larger prize awarded in the last stage (D44) | players' effort allocation (D29) |
| decreasing prizes over the first n-2 stages (D44) | total effort (D29) |