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The n-player Hirshleifer contest

Author

Listed:
  • Christian Ewerhart
  • Guang-Zhen Sun
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 fi nd 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.

Suggested Citation

  • Christian Ewerhart & Guang-Zhen Sun, 2020. "The n-player Hirshleifer contest," ECON - Working Papers 361, Department of Economics - University of Zurich, revised Oct 2023.
    • Handle: RePEc:zur:econwp:361
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Difference-form contests; Nash equilibrium; rent dissipation; all-pay auction;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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