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Equilibria Without the Survival Assumption: A Non-Standard Analysis Approach

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  • Konovalov, A.
  • Marakulin, V.

    (Tilburg University, Center for Economic Research)

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 2001-34.

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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.
  2. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
  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.
  4. Florig, Michael, 1998. "A note on different concepts of generalized equilibria," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 245-254, April.
  5. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  6. 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.
  7. Florig, M., 1999. "Core Equivalence for Hierarchic Equilibria," Papiers d'Economie Mathématique et Applications 1999.79, Université Panthéon-Sorbonne (Paris 1).
  8. MERTENS , Jean-François, 1996. "The limit-price mechanism," CORE Discussion Papers 1996050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Danilov, V. I. & Sotskov, A. I., 1990. "A generalized economic equilibrium," Journal of Mathematical Economics, Elsevier, vol. 19(4), pages 341-356.
  10. Konovalov, A., 1998. "Core Equivalence in Economies With Satiation," Discussion Paper 1998-80, Tilburg University, Center for Economic Research.
  11. 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.
  12. Dubey, Pradeep, 1980. "Nash equilibria of market games: Finiteness and inefficiency," Journal of Economic Theory, Elsevier, vol. 22(2), pages 363-376, April.
  13. Dreze, Jacques H. & Muller, Heinz, 1980. "Optimality properties of rationing schemes," Journal of Economic Theory, Elsevier, vol. 23(2), pages 131-149, October.
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