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Equilibrium existence and expected payoffs in all-pay auctions with constraints

Author

Listed:
  • Ivan Pastine
  • Tuvana Pastine

Abstract

This paper introduces constraints on player choices in a broad class of all-pay auctions by allowing for upper bounds on players’ strategy sets. It proves the existence of equilibrium and derives simple closed-form formulae for players’ expected payoffs in any equilibrium. These formulae are straightforward to calculate in applications and do not require the derivation of the equilibrium or equilibria. This may be useful because: (i) In some applications players’ expected payoffs are the main item of interest. For example, one may be concerned about the effect of a policy on the market participants. In these cases the results can be used directly, bypassing the need for the full derivation of the equilibrium. (ii) In all-pay auctions, equilibrium is typically in mixed strategies. So in applications where the full characterization of the equilibrium is of interest, finding the players’ expected payoffs is a crucial first step in the derivation of the equilibrium.

Suggested Citation

  • Ivan Pastine & Tuvana Pastine, 2022. "Equilibrium existence and expected payoffs in all-pay auctions with constraints," Open Access publications 10197/24982, School of Economics, University College Dublin.
    • Handle: RePEc:ucn:oapubs:10197/24982
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    File URL: http://hdl.handle.net/10197/24982
    File Function: Open Access version, 2022
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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