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Theorems on the core of an economy with infinitely many commodities and consumers

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  • Evren, Özgür
  • Hüsseinov, Farhad

Abstract

It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581-583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579-580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind's [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585-586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core-Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai's [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791-815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 11 (December)
Pages: 1180-1196

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Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1180-1196

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Small coalitions Core Strong core Private core Walrasian equilibrium Radner equilibrium Stability Continuity Differential information Non-separable commodity space;

References

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  1. Ezra Einy & Diego Moreno & Benyamin Shitovitz, 2001. "Competitive and core allocations in large economies with differential information," Economic Theory, Springer, vol. 18(2), pages 321-332.
  2. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2003. "On The Continuity Of Equilibrium And Core Correspondences In Economies With Differential Information," Economics Working Papers we032707, Universidad Carlos III, Departamento de Economía.
  3. Farhad Hüsseinov, 2003. "Theorems on correspondences and stability of the core," Economic Theory, Springer, vol. 22(4), pages 893-902, November.
  4. Yannelis, Nicholas C, 1991. "The Core of an Economy with Differential Information," Economic Theory, Springer, vol. 1(2), pages 183-97, April.
  5. 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.
  6. Araujo, Aloisio & Martins-da-Rocha, Victor-Filipe & Monteiro, Paulo K., 2004. "Equilibria in reflexive Banach lattices with a continuum of agents," Economics Papers from University Paris Dauphine 123456789/6273, Paris Dauphine University.
  7. Carlos Hervés-Beloso & Emma Moreno-García & Nicholas Yannelis, 2005. "Characterization and incentive compatibility of Walrasian expectations equilibrium in infinite dimensional commodity spaces," Economic Theory, Springer, vol. 26(2), pages 361-381, 08.
  8. Schmeidler, David, 1972. "A Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 579-80, May.
  9. Erik Balder & Nicholas Yannelis, 2006. "Continuity properties of the private core," Economic Theory, Springer, vol. 29(2), pages 453-464, October.
  10. Cornwall, Richard R., 1969. "The use of prices to characterize the core of an economy," Journal of Economic Theory, Elsevier, vol. 1(4), pages 353-373, December.
  11. Filipe Martins-da-Rocha, V., 2003. "Equilibria in large economies with a separable Banach commodity space and non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 863-889, November.
  12. Tourky, Rabee & Yannelis, Nicholas C., 2001. "Markets with Many More Agents than Commodities: Aumann's "Hidden" Assumption," Journal of Economic Theory, Elsevier, vol. 101(1), pages 189-221, November.
  13. Rustichini, Aldo & Yannelis, Nicholas C., 1991. "Edgeworth's conjecture in economies with a continuum of agents and commodities," Journal of Mathematical Economics, Elsevier, vol. 20(3), pages 307-326.
  14. Grodal, Birgit, 1972. "A Second Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 581-83, May.
  15. Vind, Karl, 1972. "A Third Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 585-86, May.
  16. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
  17. Konrad Podczeck, 2003. "Core and Walrasian equilibria when agents' characteristics are extremely dispersed," Economic Theory, Springer, vol. 22(4), pages 699-725, November.
  18. Herves-Beloso, Carlos & Moreno-Garcia, Emma & Nunez-Sanz, Carmelo & Rui Pascoa, Mario, 2000. "Blocking Efficacy of Small Coalitions in Myopic Economies," Journal of Economic Theory, Elsevier, vol. 93(1), pages 72-86, July.
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Citations

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Cited by:
  1. Bhowmik, Anuj & Cao, Jiling, 2011. "On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces," MPRA Paper 35060, University Library of Munich, Germany, revised 28 Nov 2011.
  2. Bhowmik, Anuj, 2013. "Edgeworth equilibria: separable and non-separable commodity spaces," MPRA Paper 46796, University Library of Munich, Germany.
  3. Bhowmik, Anuj & Cao, Jiling, 2012. "Blocking efficiency in an economy with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 396-403.
  4. Hervés-Estévez, Javier & Moreno-García, Emma, 2012. "Some remarks on restricted bargaining sets," MPRA Paper 39385, University Library of Munich, Germany, revised 10 Jun 2012.
  5. Bhowmik, Anuj, 2014. "Core and Coalitional Fairness: The Case of Information Sharing Rule," MPRA Paper 56644, University Library of Munich, Germany.
  6. Bhowmik, Anuj & Cao, Jiling, 2011. "Infinite dimensional mixed economies with asymmetric information," MPRA Paper 35618, University Library of Munich, Germany.
  7. M. Ali Khan & Nobusumi Sagara, 2012. "Expected Maharam-Types and Lyapunov's Theorem for Vector Measures on Banach Spaces," Economics Working Paper Archive 593, The Johns Hopkins University,Department of Economics.
  8. Anuj Bhowmik & Maria Gabriella Graziano, 2014. "On Vind's Theorem for an Economy with Atoms and Infinitely Many Commodities," CSEF Working Papers 364, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  9. 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.
  10. Bhowmik, Anuj & Cao, Jiling, 2013. "Robust efficiency in mixed economies with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 49-57.
  11. Carlos Hervés-Beloso & Claudia Meo & Emma Moreno-García, 2014. "Information and size of coalitions," Economic Theory, Springer, vol. 55(3), pages 545-563, April.
  12. Bhowmik, Anuj, 2014. "Coalitional Fairness: The Case of Exact Feasibility with Asymmetric Information," MPRA Paper 52788, University Library of Munich, Germany.

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