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Equilibria without the survival assumption : a non-standard analysis approach

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Author Info
Konovalov, A.
Marakulin, V. (Tilburg University, Center for Economic Research)

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Abstract

It is well known that an equilibrium in the Arrow-Debreu model may fail to exist if a very restrictive condition called the survival assumption is not satisfied. We study two approaches that allow for the relaxation of this condition. Danilov and Sotskov (1980), and Florig (1998a) developed a concept of a generalized equilibrium based on a notion of hierarchic prices. Marakulin (1988, 1990) proposed a concept of an equilibrium with non-standard prices. In this paper, we establish the equivalence between non-standard and hierarchic equilibria. Furthermore, we show that the set of non-standard equilibria coincides with the fuzzy rejective core of an economy and is generically finite for any specified system of dividends.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 34.

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Date of creation: 2001
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Handle: RePEc:dgr:kubcen:200134

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  1. Aumann, Robert J & Dreze, Jacques H, 1986. "Values of Markets with Satiation or Fixed Prices," Econometrica, Econometric Society, vol. 54(6), pages 1271-1318, November. [Downloadable!] (restricted)
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  2. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July. [Downloadable!] (restricted)
  3. Anderson, Robert M., 1991. "Non-standard analysis with applications to economics," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 39, pages 2145-2208 Elsevier. [Downloadable!] (restricted)
  4. Danilov, V. I. & Sotskov, A. I., 1990. "A generalized economic equilibrium," Journal of Mathematical Economics, Elsevier, vol. 19(4), pages 341-356. [Downloadable!] (restricted)
  5. Florig, Michael, 1998. "A note on different concepts of generalized equilibria," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 245-254, April. [Downloadable!] (restricted)
  6. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May. [Downloadable!] (restricted)
  7. Konovalov, A., 1998. "Core equivalence in economies with satiation," Discussion Paper 80, Tilburg University, Center for Economic Research. [Downloadable!]
  8. Makarov, V. L., 1981. "Some results on general assumptions about the existence of economic equilibrium," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 87-99, March. [Downloadable!] (restricted)
  9. Kajii, Atsushi, 1996. "How to discard non-satiation and free-disposal with paper money," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 75-84. [Downloadable!] (restricted)
  10. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July. [Downloadable!] (restricted)
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  11. Dubey, Pradeep, 1980. "Nash equilibria of market games: Finiteness and inefficiency," Journal of Economic Theory, Elsevier, vol. 22(2), pages 363-376, April. [Downloadable!] (restricted)
  12. Florig, M., 1999. "Core Equivalence for Hierarchic Equilibria," Papiers d'Economie Mathématique et Applications 1999.79, Université Panthéon-Sorbonne (Paris 1).
  13. Dreze, Jacques H. & Muller, Heinz, 1980. "Optimality properties of rationing schemes," Journal of Economic Theory, Elsevier, vol. 23(2), pages 131-149, October. [Downloadable!] (restricted)
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