A Sealed-Bid Unit-Demand Auction with Put Options∗

We introduce a variant of the classic sealed-bid unit-demand auction in which each item has an associated put option. The put option of an item is held by the seller of the item, and gives the holder the right to sell the item to a specified target bidder at a specified strike price, regardless of market conditions. Unexercised put options expire when the auction terminates. In keeping with the underlying unit-demand framework, we assume that each bidder is the target of at most one put option. The details of each put option — holder, target, and strike price — are fixed and publicly available prior to the submission of unit-demand bids. We motivate our unit-demand auction by discussing applications to the reassignment of leases, and to the design of multi-round auctions. In the classic sealed-bid unit-demand setting, the VCG mechanism provides a truthful auction with strong associated guarantees, including efficiency and envy-freedom. In our setting, the strike price of an item imposes a lower bound on its price. The VCG mechanism does not accommodate such lower bound constraints, and hence is not directly applicable. Moreover, the strong guarantees associated with the VCG mechanism in the classic setting cannot be achieved in our setting. We formulate an appropriate solution concept for our setting, and devise a truthful auction for implementing this solution concept. We show how to compute the outcome of our auction in polynomial time. ∗Department of Computer Science, University of Texas at Austin, Austin, TX 78712. Supported by NSF Grant CCF–0635203 and THECB NHARP Grant 003658–0235–2007.