Optimal Allocations in Round-Robin Tournaments

42 Pages Posted: 2 Jun 2014

See all articles by Alex Krumer

Alex Krumer

University of St. Gallen

Reut Megidish

Sapir Academic College

Aner Sela

Ben-Gurion University of the Negev - Department of Economics; Centre for Economic Policy Research (CEPR)

Date Written: March 2014

Abstract

We study round-robin tournaments with three players whose values of winning are common knowledge. In every stage a pair-wise match is modelled as an all-pay auction. The player who wins in two matches wins the tournament. We characterize the sub-game perfect equilibrium for symmetric (all players have the same value) and asymmetric players (each one is either weak (low value) or strong (high value)) and prove that if the asymmetry between the players' values are relatively weak, each player maximizes his expected payoff if he competes in the first and the last stages of the tournament. Moreover, even when the asymmetry between the players' values are relatively strong, the strong players maximize their expected payoffs if they compete in the first and the last stages. We show that a contest designer who wishes to maximize the length of the tournament such that the winner of the tournament will be decided in the last stage should allocate the stronger players in the last stage. But if he wishes to maximize the players' expected total effort he should not allocate them in the last stage of the tournament.

Keywords: All-pay auctions, Round-robin tournaments

JEL Classification: D44, D72, D82

Suggested Citation

Krumer, Alex and Megidish, Reut and Sela, Aner, Optimal Allocations in Round-Robin Tournaments (March 2014). CEPR Discussion Paper No. DP9873, Available at SSRN: https://ssrn.com/abstract=2444894

Alex Krumer (Contact Author)

University of St. Gallen ( email )

St. Gallen
Switzerland

Reut Megidish

Sapir Academic College ( email )

Aner Sela

Ben-Gurion University of the Negev - Department of Economics ( email )

Beer-Sheva 84105
Israel
+972 8 647 2309 (Phone)
+972 8 647 2941 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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