Christian Groh (Department of Economics, University of Bonn, Lennestr.37, 53113 Bonn, Germany. groh@wiwi.uni-bonn.de) Benny Moldovanu (Department of Economics, University of Bonn, Lennestr. 37, 53113 Bonn, Germany; mold@uni-bonn.de) Aner Sela (Department of Economics, Ben Gurion University, Beer Sheva, Israel, anersela@bgu.ac.il) Uwe Sunde (IZA, P.O Box 7240, 53072 Bonn, Germany. sunde@iza.org.)
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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.
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Paper provided by SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich in its series Discussion Papers with number
140.
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Matthias Kräkel, 2005.
"Emotions and the Optimality of Unfair Tournaments,"
Discussion Papers
45, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
[Downloadable!]
Michael R. Baye & Dan Kovenock & Casper G. de Vries, 2008.
"Contests with Rank-Order Spillovers,"
Working Papers
2008-20, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
[Downloadable!]
Other versions:
Johannes Münster, 2006.
"Contests with Investment,"
Discussion Papers
120, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
[Downloadable!]