We study a model where multiple sellers with limited supply strategically choose both the price formation rule and the allocation rule. We show that inefficiency in this setting arises both because sellers choose to withhold the good and because they sell to lower valuation buyers despite the presence of higher valuation buyers. This contrasts with the findings of the literatures on monopolistic and competing sellers, which suggest that the only form of inefficiency that arises is from sellers choosing to withhold the good. Further, we show that both types of inefficiencies vanish as the number of sellers in the market grows large. It is an equilibrium fror all sellers to offer efficient mechanisms in the limit.

Formally, two sellers, each with unit supply, compete by offering mechanisms to buyers with private valuations. Each buyer participates in the mechanism that offers him the largest interim expected surplus, hence buyer participation at each seller is endogenous. Our main result is a sufficient (and almost necessary) condition for a seller's best response to a quasi-efficient mechanism to be quasi-efficient. Here, quasi-efficient means that conditional on a sale occurring, the good is allotted to the buyer who values the good the most. These conditions are strong; therefore there exist economically interesting settings where sellers offer non-quasi-efficient mechanisms in equilibrium.

Optimal Auctions with Financially Constrained Bidders (with Rakesh Vohra)

We consider an environment where potential buyers for a unique 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 propose constrained-efficient and revenue maximizing auctions for this setting. In general, the optimal auction requires `pooling' in the middle despite the maintained assumption of a monotone hazard rate. Further, the auctioneer will never find it desirable to subsidize bidders with low budgets.

Coarse Decision Making (with Nabil Al-Najjar)

We study decision makers who willingly forgo acts that finely vary with states, even though these acts are informationally and technologically feasible. They opt instead for coarse rules that are less sensitive to state by state variations. We model this coarse decision making as a consequence of decision makers using classical, frequentist methods to draw robust inferences from scarce data. Our central theme is that coarse decision making arises to mitigate the risk of over-fitting the data. Using this framework we are able to give a unified interpretation of many seemingly anomalous cognitive and decision making procedures, such as categorization, reliance on linear orders, and satisficing.

Optimal Dynamic Auctions (with Rakesh Vohra)

We consider a dynamic auction problem motivated by the traditional single-leg, multi-period revenue management problem. A seller with C units to sell faces potential buyers with unit demand who arrive and depart over the course of T time periods. The time at which a buyer arrives, her value for a unit as well as the time by which she must make the purchase are her private information. In this environment, we derive the revenue maximizing Bayesian incentive compatible selling mechanism.

Fair Discounting Auctions(with Kamal Jain, Rakesh Vohra)

An auctioneer sells a single unit to a group of bidders using a second price auction. A subset of these bidders possess a coupon entitling them to a discount off the winning bid in the event they win the auction. Bidders without the coupon are at a disadvantage relative to the situation when nobody has any coupons. Therefore, in a loose sense, these bidders end up sponsoring the coupon, at least partially. Furthermore the resulting allocation need not be efficient. Is there an alternative mechanism that would allow the auctioneer to offer discount coupons to a set of bidders while not harming the rest. In other words is it possible that the discount coupons are fully sponsored by the auctioneer. In this paper we propose desiderata that such a mechanism should have and bound their inefficiency.

Work In Progress:

Auctions on a Supply Chain (with J Feldman, V Mirrokni, S Muthukrishnan)

Subjective Testing (with Nabil Al-Najjar and Jonathan Weinstein)

Team Service in Restaurants (with B. Pablo Montagnes)

Strategy Proof Random Allotment (with Rahul Deb and Arunava Sen)