Commitment in first-price auctions

Yunjian Xu*, Katrina Ligett

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageAmerican English
Pages (from-to)449-489
Number of pages41
JournalEconomic Theory
Volume66
Issue number2
DOIs
StatePublished - 1 Aug 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.

Keywords

  • Collusion
  • Commitment
  • First-price auction
  • Stackelberg game
  • Subgame perfect equilibrium

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