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Existence of equilibria for economies with externalities and a measure space of consumers

  • Bernard Cornet
  • Mihaela Topuzu
Conference paper
Part of the Studies in Economic Theory book series (ECON.THEORY, volume 26)

Summary

This paper considers an exchange economy with a measure space of agents and consumption externalities, which take into account two possible external effects on consumers’ preferences: dependence upon prices and dependence upon other agents’ consumption. We first consider a model with a general externality mapping and we then treat the particular case of reference coalition externalities, in which the preferences of each agent a are influenced by prices and by the global or the mean consumption of the agents in finitely many (exogenously given) reference coalitions associated with agent a. Our paper provides existence results of equilibria in both models when consumers have transitive preferences. It extends in exchange economies the standard results by Aumann [2], Schmeidler [16], Hildenbrand [12], and previous results by Greenberg et al. [11] for price dependent preferences, Schmeidler [17] for fixed reference coalitions and Noguchi [15] for a more particular concept of reference coalitions. We also mention related results obtained independently by Balder [4].

Keywords and Phrases

Externalities Reference coalitions Measure space of agents Equilibrium 

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References

  1. 1.
    Arrow, K.J., Debreu, G: Existence of an equilibrium for a competitive economy. Econometrica 22, 265–290 (1954)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aumann, R.J.: Existence of a competitive equilibrium in markets with a continuum of traders. Econometrica 34, 1–17 (1966)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Aumann, R.J.: Measurable utility and measurable choice theorem. La Décision, Centre National de la Recherche Scientifique Paris, pp. 15–26 (1967)Google Scholar
  4. 4.
    Balder, E.J.: Existence of competitive equilibria in economies with a measure space of consumers and consumption externalities. Working paper (2003)Google Scholar
  5. 5.
    Berge, C.: Espaces topologiques, functions multivoques. Paris: Dunod 1959Google Scholar
  6. 6.
    Castaing, C., Valadier, M.: Convex analysis and measurable multifunctions. In: Dold, A., Eckmann, B. (eds.) Lecture notes in mathematics, 580. Berlin Heidelberg New York: Springer 1977Google Scholar
  7. 7.
    Cornet, B., Topuzu, M.: Equilibria and externalities. Cahiers de la MSE Université Paris 1 (2003)Google Scholar
  8. 8.
    Dunford, N., Schwartz, J.: Linear operators. New York: Interscience 1966Google Scholar
  9. 9.
    Fan, K.: Fixed-point and min-max theorems in locally convex linear spaces. Proceedings of the National Academy of Sciences USA 39, 121–126 (1952)ADSCrossRefGoogle Scholar
  10. 10.
    Glicksberg, I.L.: Generalization of Kakutani fixed-point theorem with applications to Nash equilibrium points. Proceedings of the American Mathematical Society 3, 170–174 (1952)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Greenberg, J., Shitovitz, B., Wieczorek, A.: Existence of equilibria in atomless production economies with price-dependent preferences. Journal of Mathematical Economics 6, 31–41 (1979)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Hildenbrand, W.: Existence of equilibria for economies with production and a measure space of consumers. Econometrica 38, 608–623 (1970)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Hildenbrand, W.: Core and equilibrium of a large economy. Princeton: Princeton University Press 1974Google Scholar
  14. 14.
    Khan, M.A., Vohra, M.: Equilibrium in abstract economies without ordered preferences and with a measure space of agents. Journal of Mathematical Economics 13, 133–142 (1984)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Noguchi, M.: Interdependent preferences with a continuum of agents. Journal of Mathematical Economics (forthcoming)Google Scholar
  16. 16.
    Schmeidler, D.: Competitive equilibria in markets with a continuum of traders and incomplete preferences. Econometrica 37, 578–585 (1969)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Schmeidler, D.: Equilibrium points of nonatomic games. Journal of Statistical Physics 7, 295–300 (1973)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Yannelis, N.C.: Equilibria in noncooperative models of competition. Journal of Economic Theory 41, 96–111 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Yannelis, N.C.: Weak sequential convergence in L p(μ, X). Journal of Mathematical Analysis and Applications 141, 72–83 (1989)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bernard Cornet
    • 1
    • 2
  • Mihaela Topuzu
    • 1
    • 3
  1. 1.CERMSEMUniversité Paris 1, Pantheon-SorbonneParisFrance
  2. 2.University of KansasLawrenceUSA
  3. 3.Universitatea de Vest TimişoaraRomania

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