Uniform price auction with quantity constraints

Abstract

We study the equilibria of uniform price auctions where many asymmetric bidders have flat demands up to their respective quantity constraints. We present an iterative procedure that systematically finds an equilibrium outcome as well as an ascending auction that has this outcome as a dominant strategy equilibrium outcome. Demand reduction and low price equilibrium may occur since it is advantageous for a bidder to give up some of his/her demand and get the remaining demand at a low price rather than to get his/her entire demand at a higher price. We show that a low price equilibrium is the only possible equilibrium when no bidder's quantity constraint is large enough to cover the supply.