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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, R.M., “An Elementary Core Equivalence Theorem,” Econometrica, 46 (1978), 1483–7.
Aumann, R.J., “Markets with a Continuum of Traders,” Econometrica, 34 (1964), 1–7.
Aumann, R.J. “Values of Markets with a Continuum, of Traders,” Econometrica, 43 (1975), 611–46.
Aumann, R J “An Axiomatization of the Non-Transferable Utility Value,” Econometrica, 53 (1985), 599–612.
Aumann, R.J. and M. Perles, “A Variational Problem Arising in Economics,” J. Math. Anal. Appl.12 (1965), 488–503.
Aumann, R.J. and L.S. Shapley, Values of Nonatomic Games, Princeton: Princeton University Press, 1974.
Bewley, T.F., “Edgeworth’s Conjecture” Econometrica41 (1973), 425–54.
Brown, D.J. and A. Robinson, “Nonstandard Exchange Economies,” Econometrica, 43 (1975), 41–45.
Debreu, G. and H.E. Scarf, “A Limit Theorem on the Core of an Economy,” International Economic Review4 (1963), 235–69.
Dubey, P. and A. Neyman, “Payoffs in Non-Atomic Economics: An Axiomatic Approach,” Econometrica, 52 (1984), 1129–50.
Edgeworth, F.Y. Mathematical PsychicsLondon: Kegan Paul, 1881.
Geanakoplos, J., “The Bargaining Set and Non-Standard Analysis,” Technical Report No. 1, Center on Decision and Conflict in Complex Organizations, Harvard University, 1978.
Hildenbrand, W., Core and Equilibria of a Large Economy, Princeton: Princeton University Press, 1974.
Kannai, Y., “Continuity Properties of the Core of a Market” Econometrica, 38 (1970), 791–815.
Mas-Colell, A., “An Equivalence Theorem for a Bargaining Set” Journal of Mathematical Economics18(2) (1989), 129–139.
Neyman, A. “Continuous Values Are Diagonal,” Mathematics of Operations Research2 (1977), 338–342.
Shapley, L.S., “A Value for n-Person Games,” Annals of Mathematics Studies, 28 (1953), 308–17.
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.
Shapley, L.S., “Values of Large Games. VII: A General Exchange Economy with Money,” RM-4248, The Rand Corporation, Santa Monica, California, 1964.
Shubik, M., “Edgeworth Market Games,” Annals of Mathematics Studies, 40 (1959), 267–78.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive