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On the Failure of Core Convergence in Economies with Asymmetric Information

Author

Listed:
  • 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)).

Suggested Citation

  • Roberto Serrano & Rajiv Vohra & Oscar Volij, 2000. "On the Failure of Core Convergence in Economies with Asymmetric Information," Econometric Society World Congress 2000 Contributed Papers 0141, Econometric Society.
    • Handle: RePEc:ecm:wc2000:0141
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    References listed on IDEAS

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    1. Gul, Faruk & Postlewaite, Andrew, 1992. "Asymptotic Efficiency in Large Exchange Economies with Asymmetric Information," Econometrica, Econometric Society, vol. 60(6), pages 1273-1292, November.
    2. 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.
    3. Robert M. Anderson & William R. Zame, 1997. "Edgeworth's Conjecture with Infinitely Many Commodities: L1," Econometrica, Econometric Society, vol. 65(2), pages 225-274, March.
    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. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-138, January.
    6. 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.
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    Cited by:

    1. Yusuke Kamishiro & Roberto Serrano, 2009. "Equilibrium Blocking in Large Quasilinear Economies," Working Papers wp2009_0911, CEMFI.
    2. Françoise Forges & Roberto Serrano, 2013. "Cooperative Games With Incomplete Information: Some Open Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-17.
    3. Beth Allen, 2006. "Market games with asymmetric information: the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 465-487, October.
    4. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
    5. Claudia Meo, 2009. "Existence of Edgeworth equilibria for economies with asymmetric information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 371-383, February.
    6. Yusuke Kamishiro & Roberto Serrano, 2008. "Information transmission and core convergence in quasilinear economies," Working Papers 2008-01, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    7. Yusuke Kamishiro & Roberto Serrano & Myrna Wooders, 2021. "Monopolists of scarce information and small group effectiveness in large quasilinear economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 801-827, December.
    8. Myerson, Roger B., 2007. "Virtual utility and the core for games with incomplete information," Journal of Economic Theory, Elsevier, vol. 136(1), pages 260-285, September.
    9. 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.
    10. 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.
    11. McLean, Richard & Postlewaite, Andrew, 2005. "Core convergence with asymmetric information," Games and Economic Behavior, Elsevier, vol. 50(1), pages 58-78, January.
    12. Yusuke Kamishiro & Roberto Serrano & Myrna Wooders, 2015. "Information and Small Group Effectiveness in Large Quasilinear Economies," Working Papers 2015-11, Brown University, Department of Economics.
    13. 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.
    14. Antonio Miralles & Marek Pycia, 2017. "Large vs. Continuum Assignment Economies: Efficiency and Envy-Freeness," Working Papers 950, Barcelona School of Economics.
    15. Roberto Serrano & Oscar Volij, 2008. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economic Journal, Royal Economic Society, vol. 118(532), pages 1719-1741, October.
    16. Mikhail Safronov, 2016. "A Coasian Approach to Efficient Mechanism Design," Cambridge Working Papers in Economics 1619, Faculty of Economics, University of Cambridge.
    17. repec:dau:papers:123456789/8158 is not listed on IDEAS
    18. 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.
    19. Khan, M. Ali & Qiao, Lei & Rath, Kali P. & Sun, Yeneng, 2020. "Modeling large societies: Why countable additivity is necessary," Journal of Economic Theory, Elsevier, vol. 189(C).
    20. Yusuke Kamishiro & Roberto Serrano, 2011. "Equilibrium Blocking in Large Quasilinear Economies," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 552-567, August.
    21. Carlos Hervés-Beloso & Claudia Meo & Emma Moreno-García, 2014. "Information and size of coalitions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 545-563, April.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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