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.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/1598 |
| Date | 16 August 2002 |
| Creators | McAdams, David |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Format | 346785 bytes, application/pdf |
| Relation | MIT Sloan School of Management Working Paper;4254-02 |
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