Optimal auctions with financially constrained bidders

We consider an environment where potential buyers of an indivisible good have liquidity constraints, in that they cannot pay more than their `budget' regardless of their valuation. A buyer's valuation for the good as well as her budget are her private information. We derive constrained-e±cient and revenue maximizing auctions for this setting. In general, the optimal auction requires `pooling' both at the top and in the middle despite the maintained assumption of a monotone hazard rate. Further, the auctioneer will never ¯nd it desirable to subsidize bidders with low budgets.