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The n-player Hirshleifer contest


Ewerhart, Christian; Sun, Guang-Zhen (2024). The n-player Hirshleifer contest. Games and Economic Behavior, 143:300-320.

Abstract

While the game-theoretic analysis of conflict is often based on the assumption of multiplicative noise, additive noise such as considered 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 and 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. Thus, in the limit, equilibria of the Hirshleifer contest share important properties of equilibria of the corresponding all-pay auction.

Abstract

While the game-theoretic analysis of conflict is often based on the assumption of multiplicative noise, additive noise such as considered 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 and 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. Thus, in the limit, equilibria of the Hirshleifer contest share important properties of equilibria of the corresponding all-pay auction.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Social Sciences & Humanities > Finance
Social Sciences & Humanities > Economics and Econometrics
Uncontrolled Keywords:Economics and econometrics, finance, difference-form contests, Nash equilibrium, rent dissipation, all-pay auction
Scope:Discipline-based scholarship (basic research)
Language:English
Date:1 January 2024
Deposited On:05 Jan 2024 10:39
Last Modified:31 Mar 2024 01:37
Publisher:Elsevier
ISSN:0899-8256
Additional Information:Earlier published as ECON Working Paper No. 361: https://www.zora.uzh.ch/id/eprint/189517/
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1016/j.geb.2023.11.004
Related URLs:https://www.zora.uzh.ch/id/eprint/189517/
Other Identification Number:merlin-id:24211
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)