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The n-player Hirshleifer contest


Ewerhart, Christian; Sun, Guang-Zhen (2020). The n-player Hirshleifer contest. Working paper series / Department of Economics 361, University of Zurich.

Abstract

We characterize the equilibrium set of the n-player Hirshleifer contest with homogeneous valuations. A symmetric equilibrium always exists. It necessarily corresponds to multilateral peace for sufficient noise and uses finite-support randomized strategies otherwise. Asymmetric equilibria are feasible for n≥3 contestants only, and only for sufficiently small noise. In pure strategies, any asymmetric equilibrium corresponds to one-sided dominance, but there is also a variety of payoff-inequivalent mixed-strategy equilibria for small noise. For arbitrarily small noise, at least two contestants engage in cut-throat competition, while any others become ultimately inactive. Of some conceptual interest is the observation that, for n sufficiently large, the unique equilibrium is multilateral peace.

Abstract

We characterize the equilibrium set of the n-player Hirshleifer contest with homogeneous valuations. A symmetric equilibrium always exists. It necessarily corresponds to multilateral peace for sufficient noise and uses finite-support randomized strategies otherwise. Asymmetric equilibria are feasible for n≥3 contestants only, and only for sufficiently small noise. In pure strategies, any asymmetric equilibrium corresponds to one-sided dominance, but there is also a variety of payoff-inequivalent mixed-strategy equilibria for small noise. For arbitrarily small noise, at least two contestants engage in cut-throat competition, while any others become ultimately inactive. Of some conceptual interest is the observation that, for n sufficiently large, the unique equilibrium is multilateral peace.

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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:Hirshleifer contest, Nash equilibrium, rent dissipation, difference-form contest, all-pay auction
Language:English
Date:August 2020
Deposited On:01 Sep 2020 14:18
Last Modified:27 Nov 2020 07:34
Series Name:Working paper series / Department of Economics
Number of Pages:41
ISSN:1664-705X
OA Status:Green
Official URL:https://www.econ.uzh.ch/en/research/workingpapers.html?paper-id=1043

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