Ex ante heterogeneity in all-pay many-player auctions with Pareto distribution of costs
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Ex ante heterogeneity in all-pay many-player auctions with Pareto distribution of costs Sérgio O. Parreiras1 · Anna Rubinchik2 Received: 27 April 2015 / Accepted: 17 September 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract We analyze an all-pay auction as a game of incomplete information, in which every player knows the cost of his effort and believes that the cost to each of his rivals is an independent Pareto random variable. The lower bound of its support, the cost parameter, can be different for each player and all are commonly known. Such an auction has a unique Bayesian-Nash equilibrium. The players with a relatively high cost parameter are not active in equilibrium, i.e., do not exert any effort, no matter what its cost. We study the effects of heterogeneity measured as a mean-preserving spread of cost parameters of the active players. There are two main findings. (1) Heterogeneity has no effect on the maximal effort, the distribution of which is fully determined by the average of the cost parameters. (2) Increase in heterogeneity lowers the total expected effort and the distribution of the minimal effort in terms of first-order stochastic dominance. Keywords Homogeneity · Group composition · Mean-preserving spread · Incomplete information · Private values JEL Classification D44
We would like to thank Dan Kovenock for the detailed comments and for their suggestions the anonymous referees as well as Ella Segev and participants of the Game Theory seminar at the Technion, Michigan State University, University of Queensland, the conference participants of the Operations Research Society of Israel, and of the Israeli Economic Association. The first author wishes to thank CEMS-Kellogg-NWU for its hospitality. The scientific responsibility is assumed by the authors. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00199019-01227-2) contains supplementary material, which is available to authorized users.
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Anna Rubinchik [email protected] Sérgio O. Parreiras [email protected]
1
Department of Economics, UNC at Chapel Hill, Chapel Hill, USA
2
Department of Economics, University of Haifa, Haifa, Israel
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S. O. Parreiras, A. Rubinchik
1 Introduction Several agents desire to get a prize. Each knows his own valuation, and they all share a common belief about valuations of the rivals. In order to get the prize, one has to make an irreversible investment and the one who makes the biggest investment wins the prize. This captures the essential features of numerous “competitive environments” around us. For example, the agents could be employees from the same department fighting for the only spot available to be promoted, runners in a city race striving to be the first to reach the finish line, firms investing in R&D in order to win an exclusive right to sell a new product. The objective of the competition organizer is not always the same. It can be to maximize the total effort invested by all agents as in the first example, the lowe
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