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

  • Evren, Özgür
  • Hüsseinov, Farhad

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Schmeidler, David, 1972. "A Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 579-80, May.
  2. 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.
  3. Grodal, Birgit, 1972. "A Second Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 581-83, May.
  4. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
  5. Farhad Hüsseinov, 2003. "Theorems on correspondences and stability of the core," Economic Theory, Springer, vol. 22(4), pages 893-902, November.
  6. Konrad Podczeck, 2003. "Core and Walrasian equilibria when agents' characteristics are extremely dispersed," Economic Theory, Springer, vol. 22(4), pages 699-725, November.
  7. 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.
  8. Erik Balder & Nicholas Yannelis, 2006. "Continuity properties of the private core," Economic Theory, Springer, vol. 29(2), pages 453-464, October.
  9. Aloisio Araujo & V. Martins-da-Rocha & Paulo Monteiro, 2004. "Equilibria in reflexive Banach lattices with a continuum of agents," Economic Theory, Springer, vol. 24(3), pages 469-492, October.
  10. Vind, Karl, 1972. "A Third Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 585-86, May.
  11. 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.
  12. 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.
  13. Yannelis, Nicholas C, 1991. "The Core of an Economy with Differential Information," Economic Theory, Springer, vol. 1(2), pages 183-97, April.
  14. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2005. "On the continuity of equilibrium and core correspondences in economies with differential information," Economic Theory, Springer, vol. 26(4), pages 793-812, November.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
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