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Core-stable rings in auctions with independent private values

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  • Forges, Françoise
  • Biran, Omer

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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File URL: http://basepub.dauphine.fr/xmlui/bitstream/123456789/4100/1/Stablebiddingrings.pdf
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Bibliographic Info

Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/4100.

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Date of creation: 2011
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Publication status: Published in Games and Economic Behavior, 2011, Vol. 73, no. 1. pp. 52-64.Length: 12 pages
Handle: RePEc:dau:papers:123456789/4100

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Keywords: Core; partition function game; Collusion; Auctions; Bayesian game;

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References

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  1. Robert H. Porter & J. Douglas Zona, 1992. "Detection of Bid Rigging in Procurement Auctions," NBER Working Papers 4013, National Bureau of Economic Research, Inc.
  2. Philippe Jehiel & Benny Moldovanu, 1996. "Strategic Nonparticipation," RAND Journal of Economics, The RAND Corporation, vol. 27(1), pages 84-98, Spring.
  3. d'ASPREMONT , C. & GERARD VARET, L.-A., . "Bayesian incentive compatible beliefs," CORE Discussion Papers RP -481, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Omer Biran, 2010. "Strategic Collusion in Auctions with Externalities," Working Papers hal-00505477, HAL.
  5. Forges, Françoise & Mertens, Jean-François & Vohra, Rajiv, 2002. "The ex ante incentive compatible core in the absence of wealth effects," Economics Papers from University Paris Dauphine 123456789/5454, Paris Dauphine University.
  6. Rajiv Vohra, 1997. "Incomplete Information, Incentive Compatibility and the Core," Working Papers 97-11, Brown University, Department of Economics.
  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. Mailath, George J. & Zemsky, Peter, 1991. "Collusion in second price auctions with heterogeneous bidders," Games and Economic Behavior, Elsevier, vol. 3(4), pages 467-486, November.
  9. Forges, Françoise & Barbar, Riham, 2007. "Collusion dans les enchères : quelques apports des jeux coopératifs," Economics Papers from University Paris Dauphine 123456789/158, Paris Dauphine University.
  10. Forges, Francoise & Minelli, Enrico, 2001. "A Note on the Incentive Compatible Core," Journal of Economic Theory, Elsevier, vol. 98(1), pages 179-188, May.
  11. Bernard Caillaud & Philippe Jehiel, 1998. "Collusion in Auctions with Externalities," RAND Journal of Economics, The RAND Corporation, vol. 29(4), pages 680-702, Winter.
  12. Roger Myerson, 2004. "Virtual utility and the core for games with incomplete information," Econometric Society 2004 North American Summer Meetings 659, Econometric Society.
  13. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
  14. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
  15. Patrick Bajari, 2001. "Comparing competition and collusion: a numerical approach," Economic Theory, Springer, vol. 18(1), pages 187-205.
  16. Graham, Daniel A & Marshall, Robert C, 1987. "Collusive Bidder Behavior at Single-Object Second-Price and English Auctions," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1217-39, December.
  17. McAfee, R. Preston & McMillan, John., 1990. "Bidding Rings," Working Papers 726, California Institute of Technology, Division of the Humanities and Social Sciences.
  18. Marshall, Robert C. & Marx, Leslie M., 2007. "Bidder collusion," Journal of Economic Theory, Elsevier, vol. 133(1), pages 374-402, March.
  19. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-42, February.
  20. Waehrer, Keith, 1999. "Asymmetric private values auctions with application to joint bidding and mergers," International Journal of Industrial Organization, Elsevier, vol. 17(3), pages 437-452, April.
  21. Pesendorfer, Martin, 2000. "A Study of Collusion in First-Price Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 381-411, July.
  22. 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.
  23. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
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Citations

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Cited by:
  1. Françoise Forges & Ram Orzach, 2010. "Core-stable Rings in Second Price Auctions with Common Values," Working Papers 2010.119, Fondazione Eni Enrico Mattei.
  2. Françoise Forges & Roberto Serrano, 2011. "Cooperative games with incomplete information: Some open problems," Working Papers 2011-14, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  3. Sonja Brangewitz & Sarah Brockhoff, 2012. "Stability of Coalitional Equilibria within Repeated Tax Competition," Working Papers 461, Bielefeld University, Center for Mathematical Economics.
  4. repec:pdn:wpaper:48 is not listed on IDEAS
  5. Biran, Omer, 2011. "Core stable bidding rings in independent private value auctions with externalities," MPRA Paper 32164, University Library of Munich, Germany.
  6. Omer Biran, 2013. "Strategic collusion in auctions with externalities," Theory and Decision, Springer, vol. 75(1), pages 117-136, July.

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