A bargaining-Walras approach for finite economies

Hervés-Estévez, Javier and Moreno-García, Emma (2015): A bargaining-Walras approach for finite economies.

Abstract

We give a notion of bargaining set for finite economies and show its coincidence with the set of Walrasian allocations. Moreover, we also show that justified objections equate with Walrasian objections. Our bargaining-Walras equivalence provides a discrete approach to the characterization of competitive equilibria obtained by Mas-Colell (1989) for continuum economies. Some further results highlight whether it is possible to restrict the formation of coalitions and still get the bargaining set. Finally, recasting some known characterizations of Walrasian allocations, we state additional interpretations of the bargaining set.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bargaining sets, coalitions, core, veto mechanism.
• Subjects: D - Microeconomics > D0 - General > D00 - General; D - Microeconomics > D1 - Household Behavior and Family Economics > D11 - Consumer Economics: Theory; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies

References

Anderson, R. M., Trockel, W., Zhou, L. (1997): Nonconvergence of the Mas- Colell and Zhou bargaining sets. Econometrica 65 (5), 1227–1239.

Aubin, J.P. (1979): Mathematical methods of game economic theory. North- Holland, Amsterdam, New York, Oxford.

Aumann, R.J. (1964): Markets with a continuum of traders. Econometrica 32, 39–50.

Aumann, R., Maschler, M. (1964): The bargaining set for cooperative games, in: M. Dresher, L. S. Shapley and A. W. Tucker, eds., Advances in game theory (Princeton University Press, Princeton, NJ), 443–447.

Debreu, G., Scarf, H. (1963): A limit theorem on the core of an economy. Inter- national Economic Review 4 (3), 235–246.

Dutta, B., Ray, D., Sengupta, K., Vohra, R. (1989): A consistent bargaining set. Journal of Economic Theory 49, 93–112.

Florenzano, M. (1990): Edgeworth equilibria, fuzzy core, and rquilibria of a production economy without ordered preferences. Journal of Mathematical Analysis and Applications 153, 18-36.

García-Cutrín, J., Hervés-Beloso, C. (1993): A discrete approach to continuum economies. Economic Theory 3, 577-584.

Grodal, B. (1972): A second remark on the core of an atomless economy. Econometrica 40, 581–583.

Hervés-Beloso, C., Moreno-García, E. (2001): “The veto mechanism revisited”; in Approximation, Optimization and Mathematical Economics; p. 147-159. Marc Lassonde (Ed.). Heidelberg, New York. Physica-Verlag.

Hervés-Beloso, C., Moreno-García, E. and N.C. Yannelis (2005a): An equivalence theorem for a differential information economy. Journal of Mathematical Economics 41 844-856.

Hervés-Beloso, C., Moreno-García, E., Yannelis, N.C. (2005b): Characterization and incentive compatibility of Walrasian expectations equilibrium in infinite dimensional commodity spaces. Economic Theory, 26, 361-381.

Hervés-Beloso, C., Moreno-García, E. (2009): Walrasian analysis via two-player games. Games and Economic Behavior 65, 220–233.

Hervés-Estévez, J., Moreno-García, E. (2015): On restricted bargaining sets. International Journal of Game Theory. DOI: 10.1007/s00182-014-0447-5.

Liu, J., Liu, X. (2012): Fuzzy extensions of bargaining sets and their existence in cooperative fuzzy games. Fuzzy sets and systems 188, 88–101.

Mas-Colell, A. (1989): An equivalence theorem for a bargaining set. Journal of Mathematical Economics 18, 129–139.

Schjødt, U., Sloth, B. (1994): Bargaining sets with small coalitions. International Journal of Game Theory 23, 49–55.

Schmeidler, D. (1972): A remark on the core of an atomless economy. Econometrica 40, 579–580.

Vind, K. (1972): A third remark on the core of an atomless economy. Econometrica 40, 585–586.

Yang, W., Liu, J., Liu, X. (2011): Aubin cores and bargaining sets for convex cooperative fuzzy games. International Journal of Game Theory 40, 467–479.