110 Ascending multi-item auction of items. The academic study of auctions grew out of the pioneering work of Vickrey(1961) and has blossomed into an enormously important area of economic research over the last few decades. Standard auction theory assumes that all potential bidders are able to pay up to their values on the items for sale. However in reality buyers may face budget constraints for a variety of reasons and therefore may be unable to afford what the items are worth to them. As stressed by Maskin(2000) in his Marshall lecture, the consideration of financial constraints on buyers is particularly relevant and important in many developing countries, where auctions are used to privatize state assets for the promotion of efficiency, competition and development, but entrepreneurs may often be financially constrained. Financial constraints not only occur in developing countries but also in developed nations. In particular, Che& Gale(1998) have discussed a variety of situations where financial constraints may arise, ranging from an agent’s moral hazard problem, business downturns and financial crises, to the acquisition decisions in many organizations which delegate to their purchasing units but impose budget constraints to control their spending, and to the case of salary caps in many professions where budget constraints are used to relax competition. Financial constraints can pose a serious obstacle to the efficient allocation of resources. For instance, financial constraints seem to have played an impor­tant role in the outcome of auctions for selling spectrum licenses conducted in US(see McMillan, 1994; Salant, 1997) and in European countries(see Illing & Klu¨h, 2003). In this paper, we study a general model in which a number of (indivisible) items are sold to a group of financially constrained bidders. Each bidder wants to consume at most one item. When no bidder faces a financial constraint, the model reduces to the well-known assignment model as studied by Koopmans& Beckmann(1957), Shapley& Shubik(1972), Crawford& Knoer(1981), Leonard(1983), and Demange et al.(1986) among others. Each bidder has private information about his values for the items and his budget and is unwilling to reveal such information for strategic reasons. In particular the auctioneer(seller) does not know the values and budgets of the bidders. It is well-known that even when a single item is auctioned, it is generally impossible to specify a mechanism which achieves full market efficiency when bidders face budget constraints. Of course, this observation also holds when there are multiple items for sale. Even worse, when bidders face financial constraints, a Walrasian equilibrium typically fails to exist, 1 and allocation 1 Besides budget constraints, price rigidities or fixed prices can also cause the failure of Walrasian Journal of Mechanism and Institution Design (), 2016