Monotone Equilibrium in Multi-Unit Auctions

David McAdams

No 4254-02, Working papers from Massachusetts Institute of Technology (MIT), Sloan School of Management

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.

Keywords: Equilibrium; Auctions (search for similar items in EconPapers)
Date: 2002-08-16
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Citations: View citations in EconPapers (1)

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