Abstract
We study exchange economies where the preference relation of each consumer depends also on the consumptions of the other consumers. In the setting of economies with a finite number \(n\ge 2\) of consumers and non-ordered and discontinuous preferences, we give sufficient and necessary conditions for the existence of alpha-core allocations in the sense of Yannelis (Equilibrium theory in infinite dimensional spaces, 102–123, 1991). The result has been obtained by means of the Ky Fan minimax inequality.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aumann, R.J.: The core of a cooperative game without side payments. Trans. Am. Math. Soc. 98, 539–552 (1961)
Basile, A., Scalzo, V.: Non-emptiness of the alpha-core: sufficient and necessary conditions. Internat. J. Game Theory 49(4), 1143–1153 (2020)
Baye, M.R., Tian, G., Zhou, J.: Characterizations of the existence of equilibria in games with discontinuous and non-quasiconcave payoffs. Rev. Econ. Stud. 60, 935–948 (1993)
Border, K.C.: A core existence theorem for games without ordered preferences. Econometrica 52(6), 1537–1542 (1984)
Borglin, A.: Price characterization of stable allocations in exchange economies with externalities. J. Econ. Theory 6(5), 483–494 (1973)
Drakopoulos, S.A.: The history of attitudes towards interdependent preferences. J. Hist. Econ. Thought 34(4), 541–557 (2012)
Duesenberry, J.S.: Income, Saving, and the Theory of Consumer Behavior. Harvard University Press, Harvard (1949)
Dupor, B., Liu, W.F.: Jealousy and equilibrium overconsumption. Am. Econ. Rev. 93(1), 423–428 (2003)
Fan, K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequalities, vol. 3. Academic Press, New York (1972)
Holly, C.: An exchange economy can have an empty alpha-core. Econ. Theor. 4, 453–461 (1994)
Martins-da-Rocha, F., Nicholas C. Yannelis, N.C.: Non-emptiness of the alpha-core, mimeo Rio de Janeiro (2011)
Nassah, R., Tian, G.: Existence of Nash equilibrium in discontinuous games. MPRA Paper No. 41206, online at https://mpra.ub.uni-muenchen.de/41206/ (2008)
Nassah, R., Tian, G.: On the existence of Nash equilibrium in discontinuous games. Econ. Theory 61(3), 515–540 (2016)
Ok, E.A., Koçkesen, L.: Negatively interdependent preferences. Soc. Choice Welf. 17, 533–558 (2000)
Reiter, S.: Interdependent preferences and groups of agents. J. Public Econ. Theory 3(1), 27–67 (2001)
Reny, P.J.: Further Results on the Existence of Nash Equilibria in Discontinuous Games. University of Chicago, Mimeo (2009)
Reny, P.J.: Nash equilibrium in discontinuous games. Econ. Theory 61(3), 553–569 (2016)
Scalzo, V.: Essential equilibria of discontinuous games. Econ. Theory 54(1), 27–44 (2013)
Scalzo, V.: Equilibrium existence in games: slight single deviation property and Ky Fan minimax inequality. J. Math. Econ. 82, 197–201 (2019)
Scalzo, V.: Existence of strong equilibrium in discontinuous games. J. Math. Anal. Appl. 491(1), Article 124247 (2020)
Scarf, H.: The core of an \(N\)-person game. Econometrica 54, 1039–1054 (1967)
Scarf, H.: On the existence of a cooperative solutions for a general class of \(n\)-person games. J. Econ. Theory 3, 169–181 (1971)
Tian, G.: Necessary and sufficient conditions for maximization of a class of preference relations. Rev. Econ. Stud. 60, 949–958 (1993)
Tian, G., Yang, L.: Theory of negative consumption externalities with applications to the economics of happiness. Econ. Theor. 39(3), 399–424 (2009)
Veblen, T.: The Theory of the Leisure Class: An Economic Study of Institutions. New York: The Modern Library (1934) [1899]
Yannelis, N.C.: The core of an economy without ordered preferences. In “Equilibrium Theory in Infinite Dimensional Spaces”, M.A. Khan and N. Yannelis, Eds., 102 - 123 (1991)
Zhao, J.: The hybrid equilibria and core selection in exchange economies with externalities. J. Math. Econ. 26(4), 387–407 (1996)
Acknowledgements
The author is grateful to referees for their valuable comments on an early version of the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Scalzo, V. Existence of alpha-core allocations in economies with non-ordered and discontinuous preferences. Econ Theory Bull 10, 1–12 (2022). https://doi.org/10.1007/s40505-022-00223-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40505-022-00223-5
Keywords
- Exchange economies with interdependent preferences
- Non-ordered preferences
- Alpha-core allocations
- Ky Fan minimax inequality