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On solution of a class of equilibrium problems

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Abstract

In the article we discuss the question of reducing the Arrow-Debreu model [1, 2] to a problem of mathematical programming; we also study conditions under which the problem is convex. The interest to the question is aroused by the circumstance that the equilibrium problems turn rather difficult for numeric solution. Two approaches are used most frequently. One is based on the monotonicity property (formulated somehow) of the excessive demand [2–5]. If this property is satisfied, then the corresponding differential system, which has the sought equilibrium at the rest point, appears stable. The other approach consists in constructing the so-called heuristic methods (see, for instance, [6]) which have more or less reasonable grounds but in general do not guarantee that a solution is obtainable.

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References

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  6. V. P. Busygin, “Computation of equilibria in piecewise-linear exchange models on the base of a sequence of linear programming problems,” in: Methods of Optimization in Economic-Mathematical Modeling [in Russian], Nauka, Moscow, 1991, pp. 41–49.

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Authors and Affiliations

  1. Moscow

    V. A. Bulavskiî

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  1. V. A. Bulavskiî
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Additional information

The research was supported by the Russian Foundation for Fundamental Research (Grant 93-012-842).

Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 35, No. 5, pp. 990–999, September–October, 1994.

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Bulavskiî, V.A. On solution of a class of equilibrium problems. Sib Math J 35, 878–886 (1994). https://doi.org/10.1007/BF02104565

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  • DOI: https://doi.org/10.1007/BF02104565

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