Optimal Seedings in Elimination Tournaments

Arbeitspapier

We study an elimination tournament with heterogenous contestants whose ability is common-knowledge. Each pair-wise match is modeled as an all-pay auction where the winner gets the right to compete at the next round. Equilibrium efforts are in mixed strategies, yielding rather complex play dynamics: the endogenous win probabilities in each match depend on the outcome of other matches through the identity of the expected opponent in the next round. The designer can seed the competitors according to their ranks. For tournaments with four players we find optimal seedings with respect to three different criteria: 1) maximization of total effort in the tournament; 2) maximization of the probability of a final among the two top ranked teams; 3) maximization of the win probability for the top player. In addition, we find the seedings ensuring that higher ranked players have a higher probability to win the tournament. Finally, we compare the theoretical predictions with data from NCAA basketball tournaments.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB/TR 15 Discussion Paper ; No. 140

Classification and Topics

• Classification: Wirtschaft ; Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior ; Asymmetric and Private Information; Mechanism Design ; Auctions
• Subject: Elimination tournaments ; Seedings ; All-Pay Auctions

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Groh, Christian ; Moldovanu, Benny ; Sela, Aner ; Sunde, Uwe
• Event: Veröffentlichung
• (who): Sonderforschungsbereich/Transregio 15 - Governance and the Efficiency of Economic Systems (GESY)
• (where): München
• (when): 2003

Further information

• DOI: doi:10.5282/ubm/epub.13411
• Handle: http://hdl.handle.net/10419/93766
• URN: urn:nbn:de:bvb:19-epub-13411-2
• Last update: 10.03.2025, 11:44 AM CET