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Commitment in first-price auctions

Xu, Yunjian and Ligett, Katrina (2018) Commitment in first-price auctions. Economic Theory, 66 (2). pp. 449-489. ISSN 0938-2259. http://resolver.caltech.edu/CaltechAUTHORS:20180816-074937577

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Abstract

We study a variation of the single-item sealed-bid first-price auction wherein one bidder (the leader) publicly commits to a (possibly mixed) strategy before the others submit their bids. For the case wherein all bidders’ valuations are commonly known, we fully characterize the committed mixed strategy that is optimal for the leader and find that both the leader and the follower with the highest valuation strictly benefit from the commitment, so long as the leader’s valuation is strictly higher than the second highest valuation of the followers. We further show that compared with the simultaneous first-price auction, the leader’s optimal commitment yields the same net utility benefit to both of these bidders. As a result, the two highest valued bidders’ incentives are aligned, facilitating coordination and implementation of the commitment. Finally, we provide characterization of the leader’s optimal commitment in a Bayesian setting with two bidders, leveraging the methodology developed for the complete-information setting.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00199-017-1069-5DOIArticle
https://rdcu.be/4CGnPublisherFree ReadCube access
ORCID:
AuthorORCID
Ligett, Katrina0000-0003-2780-6656
Additional Information:© 2017 Springer-Verlag GmbH Germany. Received: 13 October 2015; Accepted: 15 July 2017; Published online: 25 July 2017. The authors wish to thank Marina Agranov, John Ledyard, Bernhard von Stengel, Adam Wierman, 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 California Institute of Technology, April 2013, for their helpful comments. This research was supported in part by NSF Grants CCF-0910940 and CNS-1254169, the Charles Lee Powell Foundation, and a Microsoft Research Faculty Fellowship.
Funders:
Funding AgencyGrant Number
NSFCCF-0910940
NSFCNS-1254169
Charles Lee Powell FoundationUNSPECIFIED
Microsoft ResearchUNSPECIFIED
Subject Keywords:First-price auction; Commitment; Stackelberg game; Collusion; Subgame perfect equilibrium
Classification Code:JEL Classification: C61; C72; D44
Record Number:CaltechAUTHORS:20180816-074937577
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180816-074937577
Official Citation:Xu, Y. & Ligett, K. Econ Theory (2018) 66: 449. https://doi.org/10.1007/s00199-017-1069-5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88840
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Aug 2018 16:21
Last Modified:16 Aug 2018 16:21

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