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

  • Francoise Forges

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 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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  1. 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).
  2. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  3. Roger B. Myerson, 1981. "Mechanism Design by an Informed Principal," Discussion Papers 481, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
  5. 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.
  6. Claude d'Aspremont & Jacques Crémer & Louis-André Gérard-Varet, 2003. "Correlation, independence, and Bayesian incentives," Social Choice and Welfare, Springer, vol. 21(2), pages 281-310, October.
  7. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
  8. 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.
  9. Alkan, Ahmet & Gale, David, 1990. "The core of the matching game," Games and Economic Behavior, Elsevier, vol. 2(3), pages 203-212, September.
  10. Vohra, Rajiv, 1999. "Incomplete Information, Incentive Compatibility, and the Core," Journal of Economic Theory, Elsevier, vol. 86(1), pages 123-147, May.
  11. 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.
  12. de CLIPPEL, Geoffroy & MINELLI, Enrico, 2002. "Two-person bargaining with verifiable information," CORE Discussion Papers 2002063, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. d'Aspremont, C. & Gerard-Varet, L. -A., 1982. "Bayesian incentive compatible beliefs," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 83-103, June.
  14. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  15. 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).
  16. Martine Quinzii, 1982. "Core and Competitive Equilibria with Indivisibilities," Cowles Foundation Discussion Papers 644, Cowles Foundation for Research in Economics, Yale University.
  17. Roger B. Myerson, 1988. "Sustainable Matching Plans with Adverse Selection," Discussion Papers 767, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. Dutta, Bhaskar & Vohra, Rajiv, 2005. "Incomplete information, credibility and the core," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 148-165, September.
  19. 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).
  20. 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.
  21. Bengt Holmstrom & Roger B. Myerson, 1981. "Efficient and Durable Decision Rules with Incomplete Information," Discussion Papers 495, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  22. Wilson, Robert B, 1978. "Information, Efficiency, and the Core of an Economy," Econometrica, Econometric Society, vol. 46(4), pages 807-16, July.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
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