Thick and Thin Market Nonatomic Exchange Economies

Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 244)


Perfect competition — that situation in which no individual has the ability to influence prices — has traditionally been regarded as requiring large number of traders. Aumann [4] gave mathematical precision to a model with large numbers by regarding the set of traders as a nonatomic measure space. He showed that such a model passed a test of competitiveness whose origins go back to Edgeworth [16]: the game-theoretic solution concept of the core coincides with the market-demand-equals-supply notion of Walrasian, price-taking equilibrium. Related results are contained in [12] and [22].


Bound Linear Operator Banach Lattice Vector Measure Weak Topology Convex Space 
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  1. 1.
    Aliprantis, C.D. and D. J. Brown, Equilibria in Markets with a Riesz Space of Commodities, J. Math. Economics 11 (1983), 189–207.CrossRefGoogle Scholar
  2. 2.
    Armstrong, T. and M. Richter, The Core-Walras Equivalence, J. Economic Theory 33(1984), 116–151.CrossRefGoogle Scholar
  3. 3.
    Aubin, J., Mathematical Methods of Game and Economic Theory, North-Holland, Amsterdam, 1979.Google Scholar
  4. 4.
    Aumann, R. J., Markets with a continuum of traders, Econometrica 32(1964), 39–50.CrossRefGoogle Scholar
  5. 5.
    Bartle, R. J., A general bilinear vector integral, Studia Math. 15(1956), 337–352.Google Scholar
  6. 6.
    Bewley, T., The equality of the core and the set of equilibria in economies with infinitely many commodities and a continuum of agents, International Economic Review 14(1973), 383–394.CrossRefGoogle Scholar
  7. 7.
    Bourgain, J., Dunford-Pettis operators on L1 and the Radon-Nikodym property, Israel J. Math. 37(1980), 34–47.CrossRefGoogle Scholar
  8. 8.
    Chamberlin, E., The Theory of Monopolistic Competition, Harvard University Press, Cambridge, MA, 1962.Google Scholar
  9. 9.
    Cornwall, R., The use of prices to characterize the core of an economy, J. Economic Theory 1(1969), 353–373.CrossRefGoogle Scholar
  10. 10.
    Costé, A., Personal communication to J. J. Uhl, summarized in [13, pp. 90–93].Google Scholar
  11. 11.
    Debreu, G., Preference functions on a measure space of agents, Econometrica 35(1967), 111–122.CrossRefGoogle Scholar
  12. 12.
    Debreu, G. and H. Scarf, A limit theorem of the core on an economy, International Economic Review 4(1963), 235–246.CrossRefGoogle Scholar
  13. 13.
    Diestel, J. and J. J. Uhl Jr., Vector Measures, American Mathematical Society, Providence, 1977.Google Scholar
  14. 14.
    Dunford, N. and B. J. Pettis, Linear operators on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323–392.CrossRefGoogle Scholar
  15. 15.
    Dunford, N. and J. T. Schwartz, Linear Operators, Part I, Interscience, New York & London, 1958.Google Scholar
  16. 16.
    Edgeworth, F. Y., Mathematical Psychics, Kegan Paul (London) 1881.Google Scholar
  17. 17.
    Ellickson, B., Indivisibility, housing markets and public goods, in Research in Urban Economics (Ed., J. Henderson), JAI Press, 1983.Google Scholar
  18. 18.
    Gelfand, I.M., Abtrakte Functionen und Lineare Operatoren, Math. Sbornik (N.S. 4) 46(1938), 235–286.Google Scholar
  19. 19.
    Gretsky, N. E. and J. M. Ostroy, The compact range property, 1984, forthcoming.Google Scholar
  20. 20.
    Hart, O., Monopolistic competition in a large economy with differentiated commodities, Review of Economic Studies 46(1979), 1–30.CrossRefGoogle Scholar
  21. 21.
    Hart, O., Monopolistic competition in the spirit of Chamberlin: A general model, ICERD Discussion Paper, 1983.Google Scholar
  22. 22.
    Hildenbrand, W., Core and Equilibria of a Large Economy, Princeton University Press, 1974.Google Scholar
  23. 23.
    Hildenbrand, W. and A. Kirman, Size removes inequity, Review of Economic Studies 30 (1973), 305–314.CrossRefGoogle Scholar
  24. 24.
    Ionescu Tulcea, A. &C., Topics in the Theory of Lifting, Springer-Verlag, New York, 1969.CrossRefGoogle Scholar
  25. 25.
    Jones, L., Existence of equilibria with infinitely many consumers and infinitely many commodities, J. Math. Economics 12(1983), 119–139.CrossRefGoogle Scholar
  26. 26.
    Klee, V., The support property of a convex set in a normal linear space, Duke Math. J. 15(1948), 767–772.CrossRefGoogle Scholar
  27. 27.
    Kluvanek, I., The range of a vector-valued measure, Math. Systems Theory 7(1973), 44–54.CrossRefGoogle Scholar
  28. 28.
    Kupka, J., Radon-Nikodym theorems and vector-valued measures, Trans. Amer. Math. Soc. 169(1972), 197–217.CrossRefGoogle Scholar
  29. 29.
    Mas-Colell, A., A model of equilibrium with differentiated commodities, J. Math. Economics 2(1975), 263–296.CrossRefGoogle Scholar
  30. 30.
    Mas-Colell, A., The price equilibrium existence problem in Banach lattices, Harvard University Discussion Paper, 1983.Google Scholar
  31. 31.
    Ostroy, J. M., Representations of large economies: The equivalence theorem, unpublished manuscript, 1973.Google Scholar
  32. 32.
    Ostroy, J. M., A reformulation of the marginal productivity theory of distribution, Econometrica 52(1984), 599–630.CrossRefGoogle Scholar
  33. 33.
    Ostroy, J. M., On the existence of Walrasian equilibrium in large-square economies, J. Math. Economics 13(1984), 143–163.CrossRefGoogle Scholar
  34. 34.
    Peressini, A. L., Ordered Topological Vector Spaces, Harper & Row, New York & London, 1967.Google Scholar
  35. 35.
    Richter, M., Coalitions, core and competition, J. Economic Theory 3(1971), 323–334.CrossRefGoogle Scholar
  36. 36.
    Schaefer, H. H., Banach Lattices and Positive Operators, Springer-Verlag, Berlin & New York, 1974.CrossRefGoogle Scholar
  37. 37.
    Talagrand, M., Dual Banach lattices with the Radon-Nikodym property, Israel J. Math. 38(1981), 46–50.CrossRefGoogle Scholar
  38. 38.
    Talangrad, M., Pettis Integral and Measure Theory, Memoirs Amer. Math. Soc., No. 307, 1984.Google Scholar
  39. 39.
    Vind, K., Edgeworth allocations in an exchange economy with many traders, International Economic Review 5(1964), 165–177.CrossRefGoogle Scholar
  40. 40.
    Yannelis, N. and W. Zame, Equilibria in Banach lattices without ordered preferences, Institute for Mathematics and its Applications-University of Minnesota Preprint Series No. 71, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at RiversideRiversideUSA
  2. 2.Department of EconomicsUniversity of California at Los AngelesLos AngelesUSA

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