Monotone Equilibrium in Multi-Unit Auctions
Name
Monotone Equilibrium in Multi-Unit 4254-02.pdf
Size
338.66 KB
Format
Adobe PDF
Checksum (MD5)
657ed3f275707e51d1e08c43e11a332d
Author(s)
McAdams, David
Date Issued
August 16, 2002
Series/Report no.
MIT Sloan School of Management Working Paper;4254-02
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.
Subjects
Equilibrium
Auctions
Persistent DSpace Link
