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Second chance offers in auctions

Author

Listed:
  • Aniruddha Bagchi
  • Brett Katzman
  • Timothy Mathews

Abstract

This paper examines situations in which a seller might make a second chance (take-it-or-leave-it) offer to a non-winning bidder at a price equal to their bid at auction. This study is motivated by the take-it-or-leave-it second chance offer rules used by eBay and a number of state procurement agencies. Equilibrium bidder behavior is determined for IPV sealed bid first price, second price, English, and Vickrey auctions when a second chance offer will be made with an exogenous probability $$p$$ . In all but the Vickrey auction (which elicits the dominant strategy of bidding one’s value) equilibrium bids are lower than if there were no possibility of a second chance offer and higher than if a second chance offer will be made for certain. Further, the possibility of a second chance offer erodes the strategic equivalence between second price bids and English auction drop out levels. If bidders are risk averse (with CRRA preferences), this difference leads to expected revenue dominance of the second price over the English auction, both of which dominate the Vickrey auction. The first price auction is also shown to revenue dominate the Vickrey auction, and moreover, numerical results and intuition from existing literature suggest that the first price auction revenue dominates the second price auction. Copyright Springer-Verlag Wien 2014

Suggested Citation

  • Aniruddha Bagchi & Brett Katzman & Timothy Mathews, 2014. "Second chance offers in auctions," Journal of Economics, Springer, vol. 112(1), pages 1-29, May.
    • Handle: RePEc:kap:jeczfn:v:112:y:2014:i:1:p:1-29
    DOI: 10.1007/s00712-012-0330-4
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    References listed on IDEAS

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    1. Jeroen M. Swinkels, 1999. "Asymptotic Efficiency for Discriminatory Private Value Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 509-528.
    2. Engelbrecht-Wiggans, Richard & Kahn, Charles M., 1998. "Multi-Unit Pay-Your-Bid Auctions with Variable Awards," Games and Economic Behavior, Elsevier, vol. 23(1), pages 25-42, April.
    3. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    4. Jeitschko, Thomas D., 1999. "Equilibrium price paths in sequential auctions with stochastic supply," Economics Letters, Elsevier, vol. 64(1), pages 67-72, July.
    5. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
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    Cited by:

    1. Minbo Xu & Sanxi Li & Jianye Yan, 2019. "All‐Pay Auctions With A Buy‐Price Option," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 617-630, January.

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    More about this item

    Keywords

    Auctions; Second chance offer; Internet; D44; C70;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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