Optimal Auctions with Budget Constraints
4We 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-efficient and revenue maximizing auctions for this setting. In general, the optimal auction requires ΓÇÿpoolingΓÇÖ both at the top and in the middle despite the maintained assumption of a monotone hazard rate. Further, the auctioneer will never find it desirable to offer lump sum subsidies to bidders with low budgets. On a technical note, our analysis is based on the `reduced formΓÇÖ representation of auctions, which enables one to exploit a polymatroid representation of auctions. This polymatroid representation is useful in other applications, time permitting, will be outlined.