Commitment in First-Price Auctions

We study a variation of the single-item sealed-bid first-price auction wherein one bidder (the leader) publicly commits to a strategy before the others submit their bids. We fully characterize the committed mixed strategy that is optimal for the leader, and find that the leader and the follower with the highest valuation strictly benefit from the commitment. We further show that compared with the simultaneous first-price auction, the leader’s optimal commitment yields the same net utility benefit to each of the two highest-valued bidders. As a result, these two bidders’ incentives are aligned, facilitating coordination and implementation of the commitment. ∗Corresponding author. Engineering Systems and Design, Singapore University of Technology and Design; [email protected]. †Division of the Humanities and Social Sciences, California Institute of Technology; [email protected]. The authors wish to thank Marina Agranov, John Ledyard, Bernhard von Stengel, Adam Wierman, John Wooders, and the participants of Dagstuhl seminar on the Interface of Computation, Game Theory, and Economics at Wadern, Germany, April 2013, and the Social Sciences Brown Bag Seminar at Califnornia Institute of Technology, April 2013, for their helpful comments. This research was supported in part by the MIT-SUTD International Design Center (IDC) Grant IDG21400103, NSF grants CCF-0910940 and CNS-1254169, the Charles Lee Powell Foundation, and a Microsoft Research Faculty Fellowship.