Existence of equilibrium in a discriminatory price auction

In this paper, we examine a specific discriminatory price auction of Y divisible objects. Players have demand schedules for the objects and are allowed to bid any amount in the interval [0, Y]. This game describes the main features of Treasury bill auctions. We characterize the set of Nash equilibria of this game. In particular, Nash equilibria may not exist unless bidders face demand functions satisfying special restrictions. This result raises questions about using the theory of auctions of single objects to predict the outcome of multi-object auctions. Copyright © 2009 Elsevier B.V. All rights reserve