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

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  • Francoise Forges

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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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 1686.

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

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Keywords: core; incentive compatible mechanism; indivisible goods; private information;

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  1. de CLIPPEL, Geoffroy & MINELLI, Enrico, 2002. "Two-person bargaining with verifiable information," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2002063, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Myerson Roger B., 1995. "Sustainable Matching Plans with Adverse Selection," Games and Economic Behavior, Elsevier, Elsevier, vol. 9(1), pages 35-65, April.
  3. FORGES, Françoise & MINELLI, Enrico, . "A note on the incentive compatible core," CORE Discussion Papers RP -1523, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. F. Forges, 2002. "The Ex Ante Incentive Compatible Core of the Assignment Game," THEMA Working Papers 2002-07, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  5. d'Aspremont, C. & Gerard-Varet, L. -A., 1982. "Bayesian incentive compatible beliefs," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 83-103, June.
  6. Bhaskar Dutta & Rajiv Vohra, 2001. "Incomplete Information, Credibility and the Core," Working Papers 2001-02, Brown University, Department of Economics.
  7. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, Econometric Society, vol. 56(6), pages 1247-57, November.
  8. Martine Quinzii, 1982. "Core and Competitive Equilibria with Indivisibilities," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 644, Cowles Foundation for Research in Economics, Yale University.
  9. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 182R, Cowles Foundation for Research in Economics, Yale University.
  10. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 345-61, March.
  11. Rajiv Vohra, 1997. "Incomplete Information, Incentive Compatibility and the Core," Working Papers 97-11, Brown University, Department of Economics.
  12. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, Econometric Society, vol. 51(6), pages 1799-819, November.
  13. Alkan, Ahmet & Gale, David, 1990. "The core of the matching game," Games and Economic Behavior, Elsevier, Elsevier, vol. 2(3), pages 203-212, September.
  14. Francoise Forges & Enrico Minelli & Rajiv Vohra, 2000. "Incentives and the Core of an Exchange Economy: A Survey," Working Papers 2000-22, Brown University, Department of Economics.
  15. Francoise Forges & Jean-Francois Mertens & Rajiv Vohra, 2002. "The Ex Ante Incentive Compatible Core in the Absence of Wealth Effects," Econometrica, Econometric Society, Econometric Society, vol. 70(5), pages 1865-1892, September.
  16. Roger B. Myerson, 1981. "Mechanism Design by an Informed Principal," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 481, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  17. Johnson, Scott & Pratt, John W & Zeckhauser, Richard J, 1990. "Efficiency Despite Mutually Payoff-Relevant Private Information: The Finite Case," Econometrica, Econometric Society, Econometric Society, vol. 58(4), pages 873-900, July.
  18. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 100(2), pages 295-328, October.
  19. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  20. d'ASPREMONT, Claude & CREMER, Jacques & GERARD-VARET, Louis-André, . "Incentives and the existence of Pareto-optimal revelation mechanisms," CORE Discussion Papers RP -902, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  21. Garratt, Rod & Qin, Cheng-Zhong, 1996. "Cores and Competitive Equilibria with Indivisibilities and Lotteries," Journal of Economic Theory, Elsevier, Elsevier, vol. 68(2), pages 531-543, February.
  22. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 87(2), pages 293-314, April.
  23. d ASPREMONT, Claude & CRÉMER, Jacques & GÉRARD-VARET, Louis-André, 2003. "Correlation, independence, and Bayesian incentives," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2003045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  24. d'ASPREMONT, Claude & GERARD-VARET, Louis-André, . "Incentives and incomplete information," CORE Discussion Papers RP -354, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  25. Wilson, Robert B, 1978. "Information, Efficiency, and the Core of an Economy," Econometrica, Econometric Society, Econometric Society, vol. 46(4), pages 807-16, July.
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Cited by:
  1. S. D. Flåm. & L. Koutsougeras, 2007. "Private information, transferable utility,and the core," The School of Economics Discussion Paper Series, Economics, The University of Manchester 0703, Economics, The University of Manchester.

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