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An Axiomatic Approach to the Equivalence Phenomenon

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Part of the book series: NATO ASI Series ((ASID,volume 77))

Abstract

It is a striking fact that different solutions (such as Walrasian, core and value allocations) become equivalent in perfectly competitive economies (see, e.g., [1], [2], [3], [7], [8], [9], [10], [11], [12], [13], [14], [15], [19], [20]). We attempt to understand this phenomenon by making explicit certain crucial properties that are common across these solutions and on which — at bottom — the equivalence depends.

This is a synopsis of our paper “An Equivalence Principle for Perfectly Competitive Economies,” Technical Report #34, Institute for Decision Sciences, Stony Brook (November 1993), to which we refer the reader for full details.

Support by the US-Israel Binational Science Foundation Grant No. 8500123 and by the US National Science Foundation Grant DMS-8705294 is gratefully acknowledged.

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References

  1. Anderson, R.M., “An Elementary Core Equivalence Theorem,” Econometrica, 46 (1978), 1483–7.

    Article  Google Scholar 

  2. Aumann, R.J., “Markets with a Continuum of Traders,” Econometrica, 34 (1964), 1–7.

    Article  Google Scholar 

  3. Aumann, R.J. “Values of Markets with a Continuum, of Traders,” Econometrica, 43 (1975), 611–46.

    Article  Google Scholar 

  4. Aumann, R J “An Axiomatization of the Non-Transferable Utility Value,” Econometrica, 53 (1985), 599–612.

    Google Scholar 

  5. Aumann, R.J. and M. Perles, “A Variational Problem Arising in Economics,” J. Math. Anal. Appl.12 (1965), 488–503.

    Google Scholar 

  6. Aumann, R.J. and L.S. Shapley, Values of Nonatomic Games, Princeton: Princeton University Press, 1974.

    Google Scholar 

  7. Bewley, T.F., “Edgeworth’s Conjecture” Econometrica41 (1973), 425–54.

    Google Scholar 

  8. Brown, D.J. and A. Robinson, “Nonstandard Exchange Economies,” Econometrica, 43 (1975), 41–45.

    Article  Google Scholar 

  9. Debreu, G. and H.E. Scarf, “A Limit Theorem on the Core of an Economy,” International Economic Review4 (1963), 235–69.

    Google Scholar 

  10. Dubey, P. and A. Neyman, “Payoffs in Non-Atomic Economics: An Axiomatic Approach,” Econometrica, 52 (1984), 1129–50.

    Article  Google Scholar 

  11. Edgeworth, F.Y. Mathematical PsychicsLondon: Kegan Paul, 1881.

    Google Scholar 

  12. Geanakoplos, J., “The Bargaining Set and Non-Standard Analysis,” Technical Report No. 1, Center on Decision and Conflict in Complex Organizations, Harvard University, 1978.

    Google Scholar 

  13. Hildenbrand, W., Core and Equilibria of a Large Economy, Princeton: Princeton University Press, 1974.

    Google Scholar 

  14. Kannai, Y., “Continuity Properties of the Core of a Market” Econometrica, 38 (1970), 791–815.

    Article  Google Scholar 

  15. Mas-Colell, A., “An Equivalence Theorem for a Bargaining Set” Journal of Mathematical Economics18(2) (1989), 129–139.

    Google Scholar 

  16. Neyman, A. “Continuous Values Are Diagonal,” Mathematics of Operations Research2 (1977), 338–342.

    Google Scholar 

  17. Shapley, L.S., “A Value for n-Person Games,” Annals of Mathematics Studies, 28 (1953), 308–17.

    Google Scholar 

  18. Shapley, L.S., “Utility Comparison and the Theory of Games,” in La Decision: Aggregation et Dynamique des Ordres de Preference, Paris: Editions du Centre National de la Recherche Scientifique (1969), 251–63.

    Google Scholar 

  19. Shapley, L.S., “Values of Large Games. VII: A General Exchange Economy with Money,” RM-4248, The Rand Corporation, Santa Monica, California, 1964.

    Google Scholar 

  20. Shubik, M., “Edgeworth Market Games,” Annals of Mathematics Studies, 40 (1959), 267–78.

    Google Scholar 

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© 1994 Springer Science+Business Media Dordrecht

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Dubey, P., Neyman, A. (1994). An Axiomatic Approach to the Equivalence Phenomenon. In: Mertens, JF., Sorin, S. (eds) Game-Theoretic Methods in General Equilibrium Analysis. NATO ASI Series, vol 77. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1656-7_13

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  • DOI: https://doi.org/10.1007/978-94-017-1656-7_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4442-6

  • Online ISBN: 978-94-017-1656-7

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