Cach, Josef Solution set in a special case of generalized Nash equilibrium games. (English) Zbl 1265.91007 Kybernetika 37, No. 1, 21-37 (2001). Summary: A special class of generalized Nash equilibrium problems is studied. Both variational and quasi-variational inequalities are used to derive some results concerning the structure of the sets of equilibria. These results are applied to the Cournot oligopoly problem. MSC: 91A10 Noncooperative games 90C30 Nonlinear programming Keywords:generalized Nash equilibrium problem; Cournot oligopoly problem × Cite Format Result Cite Review PDF Full Text: EuDML Link References: [1] Arrow K., Debreu G.: Existence of equilibrium for competitive economy. Econometrica 22 (1954), 265-290 · Zbl 0055.38007 · doi:10.2307/1907353 [2] Baiocchi C., Capelo A.: Variational and Quasi-Variational Inequalities. Wiley, New York 1984 · Zbl 0551.49007 [3] Cach J.: A Nonsmooth Approach to the Computation of Equilibria (in Czech). Diploma Thesis, Charles University, Prague 1996 [4] Chan D., Pang J.-S.: The generalized quasi-variational problem. Math. Oper. Res. 7 (1982), 211-222 · Zbl 0502.90080 · doi:10.1287/moor.7.2.211 [5] Debreu G.: A social equilibrium existence theorem. Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 886-893 · Zbl 0047.38804 · doi:10.1073/pnas.38.10.886 [6] Harker P. T.: A variational inequality approach for the determination of oligopolistic market equilibrium. Math. Programming 30 (1984), 105-111 · Zbl 0559.90015 · doi:10.1007/BF02591802 [7] Harker P. T.: Generalized Nash games and quasi-variational inequalities. European J. Oper. Res. 54 (1991), 81-94 · Zbl 0754.90070 · doi:10.1016/0377-2217(91)90325-P [8] Harker P. T., Pang J.-S.: Finite-dimensional variational inequalities and complementarity problems: a survey of theory, algorithms and applications. Math. Programming 60 (1990), 161-220 · Zbl 0734.90098 · doi:10.1007/BF01582255 [9] Ichiishi T.: Game Theory for Economic Analysis. Academic Press, New York 1983 · Zbl 0522.90104 [10] Mosco V.: Implicit variational problems and quasi-variational inequalities. Nonlinear Operations and the Calculus of Variations - Summer School held in Bruxelles on 8-19 September 1975 (J. P. Gossez et al, Lecture Notes in Mathematics 543.) Springer Verlag, Berlin 1976, pp. 83-156 [11] Murphy F. H., Sherali H. D., Soyster A. L.: A mathematical programming approach for determining oligopolistic market equilibrium. Math. Programming 24 (1982), 92-106 · Zbl 0486.90015 · doi:10.1007/BF01585096 [12] Nash J.: Non-cooperative games. Ann. of Math. 54 (1951), 286-295 · Zbl 0045.08202 · doi:10.2307/1969529 [13] Outrata J. V., Kočvara M., Zowe J.: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results. Kluwer, Dordrecht 1998 · Zbl 0947.90093 [14] Outrata J. V., Zowe J.: A numerical approach to optimization problems with variational inequality constraints. Math. Programming 68 (1995), 105-130 · Zbl 0835.90093 · doi:10.1007/BF01585759 [15] Rosen J. B.: Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33 (1965), 520-534 · Zbl 0142.17603 · doi:10.2307/1911749 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.