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An Ascending Auction for Independent Values: Uniqueness and Robustness to Strategic Uncertainty

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Abstract

We consider an single object auction environment with interdependent valuations and a generalized Vickrey-Clark-Groves allocation mechanism that allocates the object almost efficiently in a strict ex post equilibrium. If there is a significant amount of interdependence, there are multiple rationalizable outcomes of this direct mechanism and any other mechanism that allocates the object almost efficiently. This is true whether the agents know about each others' payoff types or not. We consider an ascending price dynamic version of the generalized VCG mechanism. When there is complete information among the agents of their payoff types, we show that the almost efficient allocation is the unique backward induction (i.e., extensive form rationalizable) outcome of the auction, even when there are multiple rationalizable outcomes in the static version. This example illustrates the role that open auctions may play in obtaining efficient allocations by reducing strategic uncertainty.

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  • Dirk Bergemann & Stephen Morris, 2007. "An Ascending Auction for Independent Values: Uniqueness and Robustness to Strategic Uncertainty," Cowles Foundation Discussion Papers 1600, Cowles Foundation for Research in Economics, Yale University, revised Mar 2007.
    • Handle: RePEc:cwl:cwldpp:1600
    Note: CFP 1207.
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    References listed on IDEAS

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    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. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    3. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, vol. 50(2), pages 285-299, April.
    4. Partha Dasgupta & Eric Maskin, 2000. "Efficient Auctions," The Quarterly Journal of Economics, Oxford University Press, vol. 115(2), pages 341-388.
    5. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    6. Guillermo Caruana & Liran Einav, 2008. "A Theory of Endogenous Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(1), pages 99-116.
    7. Gale, Douglas, 1995. "Dynamic Coordination Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 1-18, January.
    8. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    9. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
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    Cited by:

    1. Gerard van der Laan & Zaifu Yang, 2016. "An ascending multi-item auction with financially constrained bidders," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 109-149, December.
    2. Loertscher, Simon & Mezzetti, Claudio, 2021. "A dominant strategy, double clock auction with estimation-based tatonnement," Theoretical Economics, Econometric Society, vol. 16(3), July.
    3. Catonini, Emiliano & Penta, Antonio, 2022. "Backward Induction Reasoning beyond Backward Induction," TSE Working Papers 22-1298, Toulouse School of Economics (TSE).
    4. Levent Ulku, 2010. "Monotone Implementation," Working Papers 1004, Centro de Investigacion Economica, ITAM.
    5. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    6. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    7. Zaifu Yang & Jingsheng Yu, 2018. "Efficient Ascending Menu Auctions with Budget Constrained Bidders," Discussion Papers 18/09, Department of Economics, University of York.
    8. Satoru Fujishige & Zaifu Yang, 2020. "A Universal Dynamic Auction for Unimodular Demand Types: An Efficient Auction Design for Various Kinds of Indivisible Commodities," Discussion Papers 20/08, Department of Economics, University of York.
    9. Ülkü, Levent, 2014. "Implementation in an interdependent value framework," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 64-70.

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    More about this item

    Keywords

    Dynamic auction; Rationalizability; Extensive form; Uniqueness; Strategic uncertainty;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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