Monotone Equilibrium in Multi-Unit Auctions
By David McAdams. 2006
73 citations recorded by the source corpus.
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.
Subfields: Economics and Econometrics, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/ed6a6ae4aae552c705c969d25896ee70e88d5293
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In Economics and Econometrics
In Management Science and Operations Research
Citations in the corpus
- On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games (2009, background): “This permits new existence results in auctions with multi-dimensional types and multi-unit demands (see McAdams (2004)).”
- Isotone Equilibrium in Games of Incomplete Information (2002, background): “In Milgrom and Roberts (1990) and Vives (1990), a supermodular game is one in which Π i (a, t) is supermodular in a, with no conditions placed on the distribution of types. Thus, the primitive conditions of cases 1,2 are only satisfied in a subclass of supermodular (and log-supermodular) games. This”