Optimal seedings in elimination tournaments |
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Authors: | Christian Groh Benny Moldovanu Aner Sela Uwe Sunde |
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Institution: | (1) Department of Psychology, Universiteit van Amsterdam, Roetersstraat 15, 1018 WB Amsterdam, The Netherlands |
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Abstract: | We study an elimination tournament with heterogenous contestants whose ability is common-knowledge. Each pair-wise match is
modeled as an all-pay auction. Equilibrium efforts are in mixed strategies, yielding complex dynamics: endogenous win probabilities
in each match depend on other matches’ outcome through the identity of the expected opponent in the next round. The designer
seeds competitors according to their ranks. For tournaments with four players we find optimal seedings for three different
criteria: (1) maximization of total tournament effort; (2) maximization of the probability of a final among the two top ranked
teams; (3) maximization of the win probability for the top player. We also find the seedings ensuring that higher ranked players
have a higher winning probability. We compare our predictions with data from NCAA basketball tournaments. |
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