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Online Auction and List Price Revenue Management

Listed author(s):
  • René Caldentey

    ()

    (Stern School of Business, New York University, 44 West Fourth Street, New York, New York 10012)

  • Gustavo Vulcano

    ()

    (Stern School of Business, New York University, 44 West Fourth Street, New York, New York 10012)

Registered author(s):

    We analyze a revenue management problem in which a seller facing a Poisson arrival stream of consumers operates an online multiunit auction. Consumers can get the product from an alternative list price channel. We consider two variants of this problem: In the first variant, the list price is an external channel run by another firm. In the second one, the seller manages both the auction and the list price channels. Each consumer, trying to maximize his own surplus, must decide either to buy at the posted price and get the item at no risk, or to join the auction and wait until its end, when the winners are revealed and the auction price is disclosed. Our approach consists of two parts. First, we study structural properties of the problem, and show that the equilibrium strategy for both versions of this game is of the threshold type, meaning that a consumer will join the auction only if his arrival time is above a function of his own valuation. This consumer's strategy can be computed using an iterative algorithm in a function space, provably convergent under some conditions. Unfortunately, this procedure is computationally intensive. Second, and to overcome this limitation, we formulate an asymptotic version of the problem, in which the demand rate and the initial number of units grow proportionally large. We obtain a simple closed-form expression for the equilibrium strategy in this regime, which is then used as an approximate solution to the original problem. Numerical computations show that this heuristic is very accurate. The asymptotic solution culminates in simple and precise recipes of how bidders should behave, as well as how the seller should structure the auction, and price the product in the dual-channel case.

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    File URL: http://dx.doi.org/10.1287/mnsc.1060.0646
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 53 (2007)
    Issue (Month): 5 (May)
    Pages: 795-813

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    Handle: RePEc:inm:ormnsc:v:53:y:2007:i:5:p:795-813
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    1. Martin A. Lariviere & Jan A. Van Mieghem, 2004. "Strategically Seeking Service: How Competition Can Generate Poisson Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 23-40, January.
    2. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    3. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-1090, October.
    4. Glazer, Amihai & Hassin, Refael, 1983. "?/M/1: On the equilibrium distribution of customer arrivals," European Journal of Operational Research, Elsevier, vol. 13(2), pages 146-150, June.
    5. Alvin E. Roth & Axel Ockenfels, 2002. "Last-Minute Bidding and the Rules for Ending Second-Price Auctions: Evidence from eBay and Amazon Auctions on the Internet," American Economic Review, American Economic Association, vol. 92(4), pages 1093-1103, September.
    6. Edieal J. Pinker & Abraham Seidmann & Yaniv Vakrat, 2003. "Managing Online Auctions: Current Business and Research Issues," Management Science, INFORMS, vol. 49(11), pages 1457-1484, November.
    7. Jérémie Gallien & Shobhit Gupta, 2007. "Temporary and Permanent Buyout Prices in Online Auctions," Management Science, INFORMS, vol. 53(5), pages 814-833, May.
    8. Budish, Eric B. & Takeyama, Lisa N., 2001. "Buy prices in online auctions: irrationality on the internet?," Economics Letters, Elsevier, vol. 72(3), pages 325-333, September.
    9. Wang, Ruqu, 1993. "Auctions versus Posted-Price Selling," American Economic Review, American Economic Association, vol. 83(4), pages 838-851, September.
    10. Gustavo Vulcano & Garrett van Ryzin & Costis Maglaras, 2002. "Optimal Dynamic Auctions for Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 7-11.
    11. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-86, July.
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