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Optimal Sale: Auctions with a Buy-Now Option

Author

Listed:
  • Subir Bose
  • Arup Daripa

    (Department of Economics, Mathematics & Statistics, Birkbeck)

Abstract

We characterize the optimal selling mechanism in a scenario where similar goods are sold to “high end” buyers through a posted price and to “lower end” buyers through an auction. We show that the optimal mechanism involves an auction which is a standard optimal auction (Myerson (1981)) up to a critical type. Types above the critical type are pooled. Further, the allocation probability jumps up at the critical type and is the maximal possible for the pooled types. Therefore other than pooling at the top, the optimal mechanism allocates the object as efficiently as in a standard optimal auction. We show that posted price selling followed by auctions with a “temporary” buy-now option implements the optimal mechanism. Auctions with such an option are in widespread use on eBay.

Suggested Citation

  • Subir Bose & Arup Daripa, 2007. "Optimal Sale: Auctions with a Buy-Now Option," Birkbeck Working Papers in Economics and Finance 0702, Birkbeck, Department of Economics, Mathematics & Statistics.
  • Handle: RePEc:bbk:bbkefp:0702
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    File URL: http://www.bbk.ac.uk/ems/research/wp/PDF/BWPEF0702.pdf
    File Function: First version, 2007
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    Cited by:

    1. Shunda, Nicholas, 2009. "Auctions with a buy price: The case of reference-dependent preferences," Games and Economic Behavior, Elsevier, vol. 67(2), pages 645-664, November.
    2. Subir Bose & Arup Daripa, 2009. "Optimal sale across venues and auctions with a buy-now option," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(1), pages 137-168, January.

    More about this item

    Keywords

    Optimal Auction; eBay Auctions; Buy-Now Option; Posted Price; Price Discrimination;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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