Abstract
We study conditions for the existence of unblockable states for a class of models studied in a series of articles on multiregional economic systems. We describe the cooperative games that are associated to these models and reduce some questions of coalition stability of regional development plans to the appropriate game theory problems. Using the classical Scarf theorem on the nonemptiness of the cores of cooperative games, we establish quite simple conditions for the existence of unblockable states of these models of interregional economic interaction. Important roles in the realization of this approach belong to the linearity of these models and the ensuing polyhedrality of the sets of balanced plans of the regional coalitions.
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References
A. G. Rubinshtein, Modeling of the Economic Interactions in Territorial Systems (Nauka, Novosibirsk, 1983) [in Russian].
V. I. Suslov, Measuring the Effects of Interregional Interactions: Models, Methods, and Results (Nauka, Novosibirsk, 1991) [in Russian].
H. Scarf, “The Core of an N-Person Game,” Econometrica 35(1), 50–69 (1967).
A. G. Granberg, V. I. Suslov, and S. A. Suspitsyn, Multiregional Systems: Mathematical Studies in Economics (Nauka, Novosibirsk, 2007) [in Russian].
K. Aliprantis, D. Braun, and O. Bearkensho, Existence and Optimality of Competitive Equilibrium (Mir, Moscow, 1995) [in Russian].
V. A. Vasil’ev, Models of Economic Exchange and Cooperative Games (Novosibirsk. Gos. Univ., Novosibirsk, 1984) [in Russian].
H. Nikaido, Convex Structures and Economic Theory (Academic Press, New York, 1968; Mir, Moscow, 1972).
O. N. Bondareva, “Core Theory for the Game of n Players,” Vestnik Leningrad. Gos. Univ. Ser. Mat., No. 13, 141–142 (1962).
A. J. Goldman, “Decomposition and Separability Theorems for PolyhedralConvex Sets,” in Linear Inequalities and Related Questions (Inostrannaya Literatura, Moscow, 1959), pp. 162–171.
R. T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, 1970; Mir, Moscow, 1973).
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Original Russian Text © V.A. Vasil’ev, V.I. Suslov, 2009, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2009, Vol. XII, No. 4, pp. 23–34.
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Vasil’ev, V.A., Suslov, V.I. On the unblockable states of multiregional economic systems. J. Appl. Ind. Math. 4, 578–587 (2010). https://doi.org/10.1134/S1990478910040137
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DOI: https://doi.org/10.1134/S1990478910040137