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Efficient and Dominance Solvable Auctions with Interdependent Valuations

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  • Kim-Sau Chung
  • Jeffrey C. Ely

Abstract

In auction environments in which agents have private values, the Vickrey auction induces agents to truthfully reveal their preferences and selects the efficient allocation accordingly. When the agents' valuations are interdependent, various generalizations of the Vickrey auction have been found which provide incentives for truthful revelation of all private information and preserve efficiency. However, these mechanisms generally do not provide the bidders with dominant strategies. The existing literature has therefore used a stronger equilibrium solution concept. In this paper we show that while the generalized VCG mechanism admits a multiplicity of equilibria, many of which are inefficient. We give conditions under which the efficiency equilibrium is the unique outcome of iterative elimination of ex post weakly dominated strategies. With two bidders, the standard single-crossing condition is sufficient. With more than two bidders, we show by example that a strengthening of the single-crossing condition is necessary.
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Suggested Citation

  • Kim-Sau Chung & Jeffrey C. Ely, 2000. "Efficient and Dominance Solvable Auctions with Interdependent Valuations," Discussion Papers 1313, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1313
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    References listed on IDEAS

    as
    1. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
    2. Krishna, Vijay, 2003. "Asymmetric English auctions," Journal of Economic Theory, Elsevier, vol. 112(2), pages 261-288, October.
    3. Dirk Bergemann & Juuso Valimaki, 2002. "Information Acquisition and Efficient Mechanism Design," Econometrica, Econometric Society, vol. 70(3), pages 1007-1033, May.
    4. Ronald M. Harstad & Dan Levin, 1985. "A Class of Dominance Solvable Common-Value Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(3), pages 525-528.
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    Citations

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    Cited by:

    1. Dirk Bergemann & Stephen Morris, 2006. "Robust Implementation: The Case of Direct Mechanisms"," Cowles Foundation Discussion Papers 1561R, Cowles Foundation for Research in Economics, Yale University, revised May 2007.
    2. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in General Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 5, pages 195-239, World Scientific Publishing Co. Pte. Ltd..
    3. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in Direct Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 4, pages 153-194, World Scientific Publishing Co. Pte. Ltd..
    4. Barry O'Neill, 2006. "Nuclear Weapons and National Prestige," Cowles Foundation Discussion Papers 1560, Cowles Foundation for Research in Economics, Yale University.
    5. Dekel, Eddie & Wolinsky, Asher, 2003. "Rationalizable outcomes of large private-value first-price discrete auctions," Games and Economic Behavior, Elsevier, vol. 43(2), pages 175-188, May.
    6. Dirk Bergemann & Stephen Morris, 2012. "Robust Virtual Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 8, pages 263-317, World Scientific Publishing Co. Pte. Ltd..
    7. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    8. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei, 2023. "Continuous implementation with payoff knowledge," Journal of Economic Theory, Elsevier, vol. 209(C).
    9. Jeffrey C. Ely & Kim-Sau Chung, 2002. "Ex-Post Incentive Compatible Mechanism Design," Discussion Papers 1339, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October.
    11. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Cowles Foundation Discussion Papers 1519, Cowles Foundation for Research in Economics, Yale University.

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    More about this item

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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