Multiunit Pay-Your-Bid Auction with One-Dimensional Multiunit Demands

An arbitrary number of units of a good is sold to two bidders through a discriminatory auction. The bidders are homogeneous ex ante and their demand functions are two-step functions that depend on a single parameter. We characterize the symmetric Bayesian equilibrium and prove its existence and uniqueness. We compare this equilibrium with the equilibrium of the multiunit Vickrey auction and with the equilibria of the single-unit first price and second price auctions. We examine the consequences of bundling all units into one package. We study the impacts that variations of the "relative" supply have on the equilibrium, on the bidders' average payoffs per unit, and on the efficiency of the equilibrium allocation. Copyright 2003 By The Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.