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Almost common value auctions and discontinuous equilibria

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  • Gisèle Umbhauer

Abstract

In almost common value auctions, even a small private payoff advantage is usually supposed to have an explosive effect on the outcomes in a second-price sealed-bid common value auction. According to (Bikhchandani in J. Econ. Theory 46:97–119, 1988 ) and (Klemperer in Eur. Econ. Rev. 42:757–769, 1998 ) the large set of equilibria obtained for common value auction games drastically shrinks, so that the advantaged player always wins the auction, at a price that sharply decreases the seller’s payoff. Yet this result has not been observed experimentally. In this paper, we show that Bikhchandani’s equilibria are not the only equilibria of the game. By introducing discontinuities in the bids, we establish a new family of perfect equilibria with interesting properties, among them: (i) the advantaged bidder does no longer win the auction regardless of her private information, (ii) she may pay a much higher price than in Bikhchandani’s equilibria, (iii) there is no ex-post regret, (iv) the intersection with level-k reasoning is not empty. We also show that a private advantage limits the number of possible discontinuities: one can introduce any number of discontinuities in the common value auction, but this is not possible in presence of a private advantage. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Gisèle Umbhauer, 2015. "Almost common value auctions and discontinuous equilibria," Annals of Operations Research, Springer, vol. 225(1), pages 125-140, February.
    • Handle: RePEc:spr:annopr:v:225:y:2015:i:1:p:125-140:10.1007/s10479-013-1377-5
    DOI: 10.1007/s10479-013-1377-5
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    References listed on IDEAS

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    1. Bikhchandani, Sushil, 1988. "Reputation in repeated second-price auctions," Journal of Economic Theory, Elsevier, vol. 46(1), pages 97-119, October.
    2. Vincent P. Crawford & Nagore Iriberri, 2007. "Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," Econometrica, Econometric Society, vol. 75(6), pages 1721-1770, November.
    3. Susan L. Rose & John H. Kagel, 2008. "Almost Common Value Auctions: An Experiment," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 17(4), pages 1041-1058, December.
    4. Rose, Susan L. & Levin, Dan, 2008. "An experimental investigation of the explosive effect in almost common value auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 927-946, September.
    5. Klemperer, Paul, 1998. "Auctions with almost common values: The 'Wallet Game' and its applications," European Economic Review, Elsevier, vol. 42(3-5), pages 757-769, May.
    6. Levin, Dan & Kagel, John H., 2005. "Almost common values auctions revisited," European Economic Review, Elsevier, vol. 49(5), pages 1125-1136, July.
    7. Christopher Avery & John H. Kagel, 1997. "Second‐Price Auctions with Asymmetric Payoffs: An Experimental Investigation," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(3), pages 573-603, September.
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