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The Ex Ante Incentive Compatible Core in Exchange Economies with and without Indivisibilities

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Francoise Forges ()

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Abstract

The ex ante incentive compatible core of an exchange economy with private information is the (standard) core of a socially designed characteristic function, which expresses the fact that coalitions allocate goods by means of random incentive compatible mechanisms. We first survey some results in the case of perfectly divisible goods. Examples then show that the ex ante incentive compatible core can be empty, even if utility functions are quasi-linear. If, in addition to quasi-linearity, further assumptions are made (like independent private values), the non-emptiness of the core follows nevertheless from d’Aspremont and Gérard-Varet’s construction of incentive compatible, ex post efficient mechanisms. We also introduce a private information version of Shapley and Scarf’s economies with indivisible goods, and prove that the ex ante incentive compatible core is always non-empty in this framework.

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Paper provided by CESifo GmbH in its series CESifo Working Paper Series with number CESifo Working Paper No. 1686.

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Date of creation: 2006
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Handle: RePEc:ces:ceswps:_1686

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Related research
Keywords: core incentive compatible mechanism indivisible goods private information

Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

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References listed on IDEAS
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  1. Forges, Francoise, 2004. "The ex ante incentive compatible core of the assignment game," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 135-151, March. [Downloadable!] (restricted)
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  2. Myerson, Roger B, 1983. "Mechanism Design by an Informed Principal," Econometrica, Econometric Society, vol. 51(6), pages 1767-97, November. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
    Other versions:
  4. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March. [Downloadable!] (restricted)
  5. Vohra, Rajiv, 1999. "Incomplete Information, Incentive Compatibility, and the Core," Journal of Economic Theory, Elsevier, vol. 86(1), pages 123-147, May. [Downloadable!] (restricted)
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  6. Myerson Roger B., 1995. "Sustainable Matching Plans with Adverse Selection," Games and Economic Behavior, Elsevier, vol. 9(1), pages 35-65, April. [Downloadable!] (restricted)
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  7. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-57, November. [Downloadable!] (restricted)
  8. Martine Quinzii, 1982. "Core and Competitive Equilibria with Indivisibilities," Cowles Foundation Discussion Papers 644, Cowles Foundation, Yale University. [Downloadable!]
  9. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation, Yale University. [Downloadable!]
  10. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March. [Downloadable!] (restricted)
  11. Alkan, Ahmet & Gale, David, 1990. "The core of the matching game," Games and Economic Behavior, Elsevier, vol. 2(3), pages 203-212, September. [Downloadable!] (restricted)
  12. Johnson, Scott & Pratt, John W & Zeckhauser, Richard J, 1990. "Efficiency Despite Mutually Payoff-Relevant Private Information: The Finite Case," Econometrica, Econometric Society, vol. 58(4), pages 873-900, July. [Downloadable!] (restricted)
  13. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October. [Downloadable!] (restricted)
  14. d'Aspremont, Claude & Gerard-Varet, Louis-Andre, 1979. "Incentives and incomplete information," Journal of Public Economics, Elsevier, vol. 11(1), pages 25-45, February. [Downloadable!] (restricted)
  15. Forges, Francoise & Minelli, Enrico, 2001. "A Note on the Incentive Compatible Core," Journal of Economic Theory, Elsevier, vol. 98(1), pages 179-188, May. [Downloadable!] (restricted)
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  16. de Clippel, Geoffroy & Minelli, Enrico, 2004. "Two-person bargaining with verifiable information," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 799-813, November. [Downloadable!] (restricted)
  17. d'Aspremont, C. & Gerard-Varet, L. -A., 1982. "Bayesian incentive compatible beliefs," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 83-103, June. [Downloadable!] (restricted)
  18. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-819, November. [Downloadable!] (restricted)
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  19. Rajiv Vohra & Bhaskar Dutta, 2003. "Incomplete Information, Credibility and the Core," Working Papers 2003-21, Brown University, Department of Economics. [Downloadable!]
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  20. Wilson, Robert B, 1978. "Information, Efficiency, and the Core of an Economy," Econometrica, Econometric Society, vol. 46(4), pages 807-16, July. [Downloadable!] (restricted)
  21. Garratt, Rod & Qin, Cheng-Zhong, 1996. "Cores and Competitive Equilibria with Indivisibilities and Lotteries," Journal of Economic Theory, Elsevier, vol. 68(2), pages 531-543, February. [Downloadable!] (restricted)
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  22. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April. [Downloadable!] (restricted)
  23. Francoise Forges & Jean-Francois Mertens & Rajiv Vohra, 2002. "The Ex Ante Incentive Compatible Core in the Absence of Wealth Effects," Econometrica, Econometric Society, vol. 70(5), pages 1865-1892, September. [Downloadable!] (restricted)
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  24. d'Aspremont, Claude & Cremer, Jacques & Gerard-Varet, Louis-Andre, 1990. "Incentives and the existence of Pareto-optimal revelation mechanisms," Journal of Economic Theory, Elsevier, vol. 51(2), pages 233-254, August. [Downloadable!] (restricted)
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