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Core-stable rings in auctions with independent private values

Author

Listed:
  • Omer Biran

    () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

  • Francoise Forges

    () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

Abstract

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders’ final utility possibly depends on the winner’s identity. We show that such direct externalities offer a possible explanation for cartels’ structures (not) observed in practice.
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Suggested Citation

  • Omer Biran & Francoise Forges, 2011. "Core-stable rings in auctions with independent private values," Post-Print hal-00632260, HAL.
  • Handle: RePEc:hal:journl:hal-00632260
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00632260
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    References listed on IDEAS

    as
    1. Patrick Bajari, 2001. "Comparing competition and collusion: a numerical approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 187-205.
    2. Forges, Francoise & Minelli, Enrico, 2001. "A Note on the Incentive Compatible Core," Journal of Economic Theory, Elsevier, vol. 98(1), pages 179-188, May.
    3. Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September.
    4. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
    5. Bernard Caillaud & Philippe Jehiel, 1998. "Collusion in Auctions with Externalities," RAND Journal of Economics, The RAND Corporation, vol. 29(4), pages 680-702, Winter.
    6. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
    7. Forges, Francoise & Minelli, Enrico & Vohra, Rajiv, 2002. "Incentives and the core of an exchange economy: a survey," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 1-41, September.
    8. Porter, Robert H & Zona, J Douglas, 1993. "Detection of Bid Rigging in Procurement Auctions," Journal of Political Economy, University of Chicago Press, vol. 101(3), pages 518-538, June.
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    10. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    11. Riham Barbar & Françoise Forges, 2007. "Collusion dans les enchères. Quelques apports des jeux coopératifs," Revue économique, Presses de Sciences-Po, vol. 58(5), pages 965-984.
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    19. Myerson, Roger B., 2007. "Virtual utility and the core for games with incomplete information," Journal of Economic Theory, Elsevier, vol. 136(1), pages 260-285, September.
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    Citations

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    Cited by:

    1. Françoise Forges & Roberto Serrano, 2013. "Cooperative Games With Incomplete Information: Some Open Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-17.
    2. Mikhail Safronov, 2016. "A Coasian Approach to Efficient Mechanism Design," Cambridge Working Papers in Economics 1619, Faculty of Economics, University of Cambridge.
    3. Forges, Françoise & Orzach, Ram, 2011. "Core-stable rings in second price auctions with common values," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 760-767.
    4. repec:dau:papers:123456789/8158 is not listed on IDEAS
    5. Omer Biran, 2011. "Core stable bidding rings in independent private value auctions with externalities," Working Papers halshs-00608008, HAL.
    6. repec:dau:papers:123456789/7891 is not listed on IDEAS
    7. Omer Biran, 2013. "Strategic collusion in auctions with externalities," Theory and Decision, Springer, vol. 75(1), pages 117-136, July.
    8. Olga Gorelkina, 2014. "Bidder Collusion and the Auction with Target Bids," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2014_10, Max Planck Institute for Research on Collective Goods.
    9. repec:eee:poleco:v:49:y:2017:i:c:p:1-23 is not listed on IDEAS
    10. Brangewitz, Sonja & Brockhoff, Sarah, 2014. "Stability of coalitional equilibria within repeated tax competition," Center for Mathematical Economics Working Papers 461, Center for Mathematical Economics, Bielefeld University.
    11. Sonja Brangewitz & Sarah Brockhoff, 2012. "Stability of Coalitional Equilibria within Repeated Tax Competition," Working Papers CIE 48, Paderborn University, CIE Center for International Economics.
    12. Forges, Françoise, 2013. "A folk theorem for Bayesian games with commitment," Games and Economic Behavior, Elsevier, vol. 78(C), pages 64-71.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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