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Existence of Equilibrium in Auctions and Discontinuous Bayesian Games: Endogenous and Incentive Compatibility Sharing Rules

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Author Info
Jackson, Matthew O.
Swinkels, Jeroen M.

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Abstract

We consider discontinuous games with incomplete information. Auctions are a leading example. With standard tie breaking rules (or more generally, sharing rules), these games may not have equilibria. We consider sharing rules that depend on the private information of players. We show that there exists an equilibrium of an augmented game with an incentive compatible sharing rule in which players reveal their private information for the purpose of determining sharing. We also show that for a large class of private value auctions, ties never occur in the equilibrium of the augmented game. This establishes existence of equilibria in such auctions with standard tie breaking rules.

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File URL: http://www.hss.caltech.edu/SSPapers/wp1075.pdf
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Publisher Info
Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1075.

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Length: 54 pages
Date of creation: Nov 1999
Date of revision:
Publication status: Published:
Handle: RePEc:clt:sswopa:1075

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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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Related research
Keywords: Bayesian Games; Existence; Equilibrium; Endogenous Sharing; Tie Breaking; Auctions.;

References listed on IDEAS
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  1. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Blackwell Publishing, vol. 54(4), pages 569-97, October. [Downloadable!] (restricted)
  2. Leo K. Simon and William R. Zame., 1987. "Discontinuous Games and Endogenous Sharing Rules," Economics Working Papers 8756, University of California at Berkeley.
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  3. Matthew O. Jackson & James Peck, 1993. "Costly Information Acquisition," Discussion Papers 1087, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  4. Swinkels, Jeroen M, 1999. "Asymptotic Efficiency for Discriminatory Private Value Auctions," Review of Economic Studies, Blackwell Publishing, vol. 66(3), pages 509-28, July. [Downloadable!] (restricted)
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  5. Wolfgang Pesendorfer & Jeroen M. Swinkels, 1996. "Efficiency and Information Aggregation in Auctions," Discussion Papers 1168, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  6. Cramton, Peter C, 1995. "Money Out of Thin Air: The Nationwide Narrowband PCS Auction," Journal of Economics & Management Strategy, Blackwell Publishing, vol. 4(2), pages 267-343, Summer.
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  7. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 439-54, July.
  8. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Blackwell Publishing, vol. 53(1), pages 1-26, January. [Downloadable!] (restricted)
  9. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  10. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  11. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
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  12. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September. [Downloadable!] (restricted)
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