We consider a generalization of the Scarf theorem on the nonemptiness of game cores to the case of fuzzy cooperative games without side payments. We consider applications of the generalized Scarf theorem to finding the nonemptiness conditions for fuzzy cores of two market games generated by the model of pure economic exchange and the spatial regional model.
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References
V. A. Vasil’ev, “Unblocked imputations of fuzzy games. I: Existence,” J. Math. Sci., New York 246, No. 6, 844–861 (2020).
H. Scarf, “The core of an n-person game,” Econometrica 35, No. 1, 50–69 (1967).
Ch. D. Aliprantis, D. J. Brown, and O. Burkinshaw, Existence and Optimality of Competitive Equilibria, Springer, Berlin etc. (1995).
V. A. Vasil’ev, Mathematical Models of General Economic Equilibrium [in Russian], Novosibirsk State Univ. Press, Novosibirsk (2009).
I. Ekeland, Éléments d’ Économie Mathématique, Hermann, Paris (1979).
A. G. Granberg, V. I. Suslov, and S. A. Suspitsin, Multiregional Systems: Economic and Mathematical Analysis [in Russian], Sib. Nauch. Izd-vo, Novosibirsk (2007).
J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton Univ. Press, Princeton, NJ (1953).
J.-P. Aubin, Optima and Equilibria. An Introduction to Nonlinear Analysis, Springer, Berlin etc. (1993).
S. L. Pechersky and E. B. Yanovskaya, Cooperative Games: Solutions and Axioms [in Russian], SPb-Europ. Univ. Press, St. Petersbg. (2004).
O. N. Bondareva, “Core theory for n-player game” [in Russian], Vestn. Leningr. Univ. 13, No. 3, 141–142 (1962).
A. G. Rubinstein, Modeling of Economic Interrelations in Multiregional Systems [in Russian], Nauka, Novosibirsk (1983).
V. A. Vasil’ev and V. I. Suslov, “On non-blocked states in multiregional economic systems,” J. Appl. Ind. Math. 4, No. 4, 578–587 (2010).
V. A. Vasil’ev and V. I. Suslov, “Edgeworth equilibrium in a model of interregional economic relations,” J. Appl. Ind. Math. 5, No. 1, 130–143 (2011).
H. Nikaido, Convex Structures and Economic Theory, Academic Press, New York (1968).
R. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, NJ (1970).
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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 18, No. 4, 2018, pp. 3-18.
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Vasil’ev, V.A. Unblocked Imputations of Fuzzy Games. II: Nonemptiness of Cores of Two Market Games. J Math Sci 253, 455–469 (2021). https://doi.org/10.1007/s10958-021-05242-4
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DOI: https://doi.org/10.1007/s10958-021-05242-4