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On the Failure of Core Convergence in Economies with Asymmetric Information

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  • Roberto Serrano

    (Brown University)

  • Rajiv Vohra

    (Brown University)

  • Oscar Volij

    (Brown University)

Abstract

In interim economies with asymmetric information, we show a robust failure of the core convergence theorem. We begin by showing that the coarse core of Wilson (1978) does not converge to any set of price equilibrium allocations considered in the literature. To prove our main point we construct a simple example of a replicated sunspot economy with strictly convex and monotonic preferences. We also show that the coarse core may not satisfy the equal treatment property. Moreover, coarse core allocations satisfying the equal treatment property may not converge to price equilibrium allocations. The result applies to any notion of price equilibrium (including rational expectations equilibria, Radner equilibria, sunspot equilibria) in which fully informed consumers receive a consumption plan maximizing ex-post utility over the ex-post budget set. The non-convergence result holds for several different notions of the interim core proposed in the literature, including the fine core (Wilson (1978)), the private core (Yannelis (1991)), the core in the pooling case (Ichiishi and Idzik (1996), Goenka and Shell (1997)), the incentive compatible core (Vohra (1999)), the coarse+ core (Lee and Volij (forthcoming)), the core with endogenous communication (Volij (forthcoming)). This failure of core convergence is a basic consequence of asymmetric information, which at the interim stage, imposes important restrictions on coalition formation. (Informational constraints may rule out many coalitions of types of consumers that would be present in the standard Debreu and Scarf (1963) complete information framework.) In particular, our negative results do not rely on the lack of `informational smallness' of agents (at least in the sense in which this term has recently been formalized in McLean and Postlewaite (1999)).

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0141.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0141

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References

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  1. Robert M. Anderson & Walter Trockel & Lin Zhou, 1997. "Nonconvergence of the Mas-Colell and Zhou Bargaining Sets," Econometrica, Econometric Society, vol. 65(5), pages 1227-1240, September.
  2. Robert M. Anderson and William R. Zame., 1995. "Edgeworth's Conjecture with Infinitely Many Commodities," Economics Working Papers 95-235, University of California at Berkeley.
  3. Prescott, Edward C & Townsend, Robert M, 1984. "Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard," Econometrica, Econometric Society, vol. 52(1), pages 21-45, January.
  4. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457 Elsevier.
  5. Gul, Faruk & Postlewaite, Andrew, 1992. "Asymptotic Efficiency in Large Exchange Economies with Asymmetric Information," Econometrica, Econometric Society, vol. 60(6), pages 1273-92, November.
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Citations

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Cited by:
  1. Yusuke Kamishiro & Roberto Serrano, 2009. "Equilibrium blocking in large quasilinear economies," Working Papers 2009-12, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  2. de Clippel, Geoffroy, 2007. "The type-agent core for exchange economies with asymmetric information," Journal of Economic Theory, Elsevier, vol. 135(1), pages 144-158, July.
  3. Roberto Serrano & Oscar Volij, 2003. "MISTAKE IN COOPERATION:the Stochastic Stability of Edgeworth's Recontracting," Working Papers 2003-23, Brown University, Department of Economics.
  4. 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.
  5. Beth Allen, 2006. "Market games with asymmetric information: the core," Economic Theory, Springer, vol. 29(2), pages 465-487, October.
  6. Serrano, Roberto & Volij, Oscar, . "Mistakes in cooperation: the stochastic stability of edgeworth's recontracting," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/360, Universidad Carlos III de Madrid.
  7. Richard McLean & Andrew Postlewaite, 2003. "Core Convergence with Asymmetric Information," PIER Working Paper Archive 03-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. M Ali Khan, 2007. "Perfect Competition," Microeconomics Working Papers 22207, East Asian Bureau of Economic Research.
  9. Claudia Meo, 2009. "Existence of Edgeworth equilibria for economies with asymmetric information," Economic Theory, Springer, vol. 38(2), pages 371-383, February.
  10. Herves-Beloso, Carlos & Meo, Claudia & Moreno Garcia, Emma, 2011. "On core solutions in economies with asymmetric information," MPRA Paper 30258, University Library of Munich, Germany, revised 12 Apr 2011.
  11. Yusuke Kamishiro & Roberto Serrano, 2008. "Information Transmission and Core Convergence in Quasilinear Economies," Working Papers 2008-5, Brown University, Department of Economics.
  12. 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.
  13. Sun, Yeneng & Yannelis, Nicholas C., 2007. "Core, equilibria and incentives in large asymmetric information economies," Games and Economic Behavior, Elsevier, vol. 61(1), pages 131-155, October.

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