Multi-unit auctions with budgets and non-uniform valuations

Abstract

This paper proposes and studies a model of multi-unit auction that allows each bidder to specify a budget and a quantity constraint. The budget tells the auctioneer how much a bidder is willing to pay and the quantity constraint specifies the maximum number of items he wants. Unlike previous studies, which assume uniform valuation (i.e., the value of an item to a bidder is fixed, no matter how many items are allocated to him), we assume that the total value of the items allocated to a bidder stops increasing, or may even start to decrease, if the number of items exceeds his acceptable quantity. We give an auction mechanism for this model and prove that when the budgets and the quantity constraints are publicly known, then our mechanism is Pareto Optimal and Incentive Compatible. On the other hand, we show that if the quantity constraints are private, then no mechanism can be both Pareto Optimal and Incentive Compatible, even if the budgets are public. We also study the revenue generated by our mechanism. © Springer-Verlag 2012.