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Consistent solutions in exchange economies: A characterization of the price mechanism

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  • Nir Dagan

Abstract

We characterize the Walrasian allocations correspondence by means of four axioms: consistency, replica invariance, individual rationality and Pareto optimality. It is shown that for any given class of exchange economies any solution that satisfies the axioms is a selection from the Walrasian allocations with slack. Preferences are assumed to be smooth, but may be satiated and non--convex. A class of economies is defined as all economies whose agents' preferences belong to an arbitrary family (finite or infinite) of types. The result can be modified to characterize equal budget Walrasian allocations with slack by replacing individual rationality with individual rationality from equal division. The results are valid also for classes of economies in which core--Walras equivalence does not hold.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 141.

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Date of creation: Nov 1995
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Handle: RePEc:upf:upfgen:141

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Web page: http://www.econ.upf.edu/

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  1. Thomson, William & Zhou, Lin, 1993. "Consistent Solutions in Atomless Economies," Econometrica, Econometric Society, Econometric Society, vol. 61(3), pages 575-87, May.
  2. Nouweland, C.G.A.M. van den & Peleg, B. & Tijs, S.H., 1994. "Axiomatic characterizations of the Walras correspondence for generalized economies," Discussion Paper, Tilburg University, Center for Economic Research 1994-58, Tilburg University, Center for Economic Research.
  3. Bettina Klaus & Hans Peters & Ton Storcken, 1997. "Reallocation of an infinitely divisible good," Economic Theory, Springer, Springer, vol. 10(2), pages 305-333.
  4. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, Elsevier, vol. 45(2), pages 330-341, August.
  5. Nir Dagan, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Economic theory and game theory, Nir Dagan 003, Nir Dagan.
  6. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, Elsevier, vol. 63(2), pages 219-245, August.
  7. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
  8. Champsaur, Paul & Laroque, Guy, 1981. "Fair allocations in large economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(2), pages 269-282, October.
  9. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, Springer, vol. 15(3), pages 187-200.
  10. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, Elsevier, vol. 46(2), pages 237-254, December.
  11. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 589-614, May.
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Cited by:
  1. Nir Dagan, 1996. "Consistency and the Walrasian Allocations Correspondence," Economic theory and game theory, Nir Dagan 012, Nir Dagan.
  2. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, Elsevier, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506 Elsevier.
  3. Sönmez, Tayfun & Ünver, M. Utku, 2010. "House allocation with existing tenants: A characterization," Games and Economic Behavior, Elsevier, Elsevier, vol. 69(2), pages 425-445, July.

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