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The n-player Hirshleifer contest


Ewerhart, Christian; Sun, Guang-Zhen (2022). The n-player Hirshleifer contest. Working paper series / Department of Economics 361, University of Zurich.

Abstract

While the game-theoretic analysis of conflict is often based upon the assumption of multiplicative noise, additive noise such as assumed by Hirshleifer (1989) may be equally plausible depending on the application. In this paper, we examine the equilibrium set of the n-player difference-form contest with heterogeneous valuations. For high or intermediate levels of noise, the equilibrium is in pure strategies, with at most one player being active. For small levels of noise, however, we find a variety of equilibria in which some but not necessarily all players randomize. In the case of homogeneous valuations, we obtain a partial uniqueness result for symmetric equilibria. As the contest becomes increasingly decisive, at least two contestants bid up to the valuation of the second-ranked contestant, while any others ultimately drop out. In the limit, equilibria in the Hirshleifer contest converge to equilibria in the corresponding all-pay auction.

Abstract

While the game-theoretic analysis of conflict is often based upon the assumption of multiplicative noise, additive noise such as assumed by Hirshleifer (1989) may be equally plausible depending on the application. In this paper, we examine the equilibrium set of the n-player difference-form contest with heterogeneous valuations. For high or intermediate levels of noise, the equilibrium is in pure strategies, with at most one player being active. For small levels of noise, however, we find a variety of equilibria in which some but not necessarily all players randomize. In the case of homogeneous valuations, we obtain a partial uniqueness result for symmetric equilibria. As the contest becomes increasingly decisive, at least two contestants bid up to the valuation of the second-ranked contestant, while any others ultimately drop out. In the limit, equilibria in the Hirshleifer contest converge to equilibria in the corresponding all-pay auction.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C72, D72, D74
Uncontrolled Keywords:Difference-form contest, Nash equilibrium, rent dissipation, all-pay auction
Language:English
Date:October 2022
Deposited On:01 Sep 2020 14:18
Last Modified:03 Nov 2022 14:17
Series Name:Working paper series / Department of Economics
Number of Pages:38
ISSN:1664-705X
Additional Information:Revised version
OA Status:Green
Official URL:https://www.econ.uzh.ch/en/research/workingpapers.html?paper-id=1043
  • Content: Published Version
  • Language: English
  • Permission: Download for registered users
  • Description: Version August 2020
  • Content: Updated Version
  • Language: English
  • Description: Revised version October 2022