When will the Range of Prizes in Tournaments Increase in the Noise or in the Number of Players?

Yigal Gerchak () and Qi-Ming He
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Yigal Gerchak: Department of Industrial Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel
Qi-Ming He: Department of Industrial Engineering, Daltech, Dalhausie University, Halifax, N.S., Canada B3J 2X4, Canada

International Game Theory Review (IGTR), 2003, vol. 05, issue 02, 151-165

Abstract: The symmetric equilibrium resulting from the celebrated Tournament model of Lazear and Rosen has a range of compensation between winner and loser which is inversely proportional toE[f(X)], the expectation of the additive noise's density. There seems to be a belief that this functional is always increasing in the noise's variability, which would agree with economic intuition — when output is noisier it should be less worthwhile to work hard. We show that such is not the case for some distributions, and characterize classes where such is or is not the case. When the number of playersngrows, winning is more difficult so we would expect the required range of compensation to be larger. That would require thatE[f(Y)], whereY =max(X1,…,Xn-1), will decrease inn. We examine the generality of this property. Finally we explore the same issues within a multiplicative model.

Keywords: Tournaments; prizes; noise; number of players (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (24)

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DOI: 10.1142/S0219198903000957

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