Keywords: generalized Nash equilibrium problem; Cournot oligopoly problem
@article{KYB_2001_37_1_a1,
author = {Cach, Josef},
title = {Solution set in a special case of generalized {Nash} equilibrium games},
journal = {Kybernetika},
pages = {21--37},
year = {2001},
volume = {37},
number = {1},
mrnumber = {1825755},
zbl = {1265.91007},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KYB_2001_37_1_a1/}
}
Cach, Josef. Solution set in a special case of generalized Nash equilibrium games. Kybernetika, Tome 37 (2001) no. 1, pp. 21-37. http://geodesic.mathdoc.fr/item/KYB_2001_37_1_a1/
[1] Arrow K., Debreu G.: Existence of equilibrium for competitive economy. Econometrica 22 (1954), 265–290 | DOI | MR
[2] Baiocchi C., Capelo A.: Variational and Quasi-Variational Inequalities. Wiley, New York 1984 | MR
[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 | DOI | MR
[5] Debreu G.: A social equilibrium existence theorem. Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 886–893 | DOI | MR | Zbl
[6] Harker P. T.: A variational inequality approach for the determination of oligopolistic market equilibrium. Math. Programming 30 (1984), 105–111 | DOI | MR | Zbl
[7] Harker P. T.: Generalized Nash games and quasi-variational inequalities. European J. Oper. Res. 54 (1991), 81–94 | DOI | Zbl
[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 | DOI | MR
[9] Ichiishi T.: Game Theory for Economic Analysis. Academic Press, New York 1983 | MR | Zbl
[10] Mosco V.: Implicit variational problems and quasi-variational inequalities. In: Nonlinear Operations and the Calculus of Variations – Summer School held in Bruxelles on 8–19 September 1975 (J. P. Gossez et al, ed., Lecture Notes in Mathematics 543.) Springer Verlag, Berlin 1976, pp. 83–156 | MR
[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 | DOI | MR | Zbl
[12] Nash J.: Non-cooperative games. Ann. of Math. 54 (1951), 286–295 | DOI | MR | Zbl
[13] Outrata J. V., Kočvara M., Zowe J.: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results. Kluwer, Dordrecht 1998 | MR | Zbl
[14] Outrata J. V., Zowe J.: A numerical approach to optimization problems with variational inequality constraints. Math. Programming 68 (1995), 105–130 | DOI | MR | Zbl
[15] Rosen J. B.: Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33 (1965), 520–534 | DOI | MR | Zbl