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Monotone Equilibrium in Multi-Unit Auctions

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  • McAdams, David

Abstract

In a large class of multi-unit auctions of identical objects that includes the uniform-price, as-bid (or discriminatory), and Vickrey auctions, a Bayesian Nash equilibrium exists in monotone pure strategies whenever there is a finite price / quantity grid and each bidder's interim expected payoff function satisfies single-crossing in own bid and type. A stronger condition, non-decreasing differences in own bid and type, is satisfied in this class of auctions given (a) independent types and (b) risk-neutral bidders with marginal values that are (c) non-decreasing in own type and have (d) non-increasing differences in own type and others' quantities. A key observation behind this analysis is that each bidder's valuation for what he wins is always modular in own bid in any multi-unit auction in which the allocation is determined by market-clearing. This paper also provides the first proof of pure strategy equilibrium existence in the uniform-price auction when bidders have multi-unit demand and values that are not private.

Suggested Citation

  • McAdams, David, 2002. "Monotone Equilibrium in Multi-Unit Auctions," Working papers 4254-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    • Handle: RePEc:mit:sloanp:1598
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    File URL: http://hdl.handle.net/1721.1/1598
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    Cited by:

    1. Alvarez, Francisco & Mazon, Cristina, 2007. "Comparing the Spanish and the discriminatory auction formats: A discrete model with private information," European Journal of Operational Research, Elsevier, vol. 179(1), pages 253-266, May.

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