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Harker, Patrick T.

Generalized Nash games and quasi-variational inequalities. (English) Zbl 0754.90070

Eur. J. Oper. Res. 54, No. 1, 81-94 (1991).
Summary: A generalized Nash game is an \(n\)-person noncooperative game with nondisjoint strategy sets; other names for this game form include social equilibria and pseudo-Nash games. This paper explores both the qualitative and quantitative properties of such games through the use of quasi-variational inequality theory. Several interesting relationships between the variational and quasi-variational inequality forms of this class of games are described and the practical implementation of generalized Nash games are explored at length.

Cited in 1 Review
Cited in 174 Documents

MSC:

91A10 Noncooperative games
91A06 \(n\)-person games, \(n>2\)
49J40 Variational inequalities

Keywords:

computational analysis; generalized Nash game; nondisjoint strategy sets; quasi-variational inequality
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References:

[1] Arrow, K. J.; Debreu, G., Existence of an equilibrium for a competitive economy, Econometrica, 22, 265-290 (1954) · Zbl 0055.38007
[2] Baiocchi, C.; Capelo, A., Variational and Quasivariational Inequalities: Applications to Free-Boundary Problems (1984), John Wiley: John Wiley New York · Zbl 0551.49007
[3] Bard, J. F., An algorithm for solving the general bilevel programming problem, Mathematics of Operations Research, 8, 260-272 (1982) · Zbl 0516.90061
[4] Bensoussan, A., Points de Nash dans le cas de fonctionnelles quadratiques et jeux différentiels linéaires a \(N\) personnes, SIAM Journal Control, 12, 460-499 (1974) · Zbl 0254.90066
[5] Bensoussan, A.; Goursat, M.; Lions, J. L., Contrôle impulsionnel et inequations quasi-variationnelles stationnaires, Comptes Rendus des Séances de l’Académie des Sciences, 276, 1279-1284 (1973) · Zbl 0264.49004
[6] Bensoussan, A.; Lions, J. L., Nouvelle formulation de problemes de controle impulsionnel et applications, Comptes Rendus des Séances de l’Académie des Sciences, 276, 1189-1192 (1973) · Zbl 0266.49007
[7] Chan, D.; Pang, J. S., The generalized quasi-variational inequality problem, Mathematics of Operations Research, 7, 211-222 (1982) · Zbl 0502.90080
[8] Dafermos, S., An iterative scheme for variational inequalities, Mathematical Programming, 26, 40-47 (1983) · Zbl 0506.65026
[9] Gabay, D.; Moulin, H., On the uniqueness and stability of Nashequilibria in noncooperative games, (Bensoussan, A.; Kleindorfer, P.; Tapiero, C. S., Applied Stochastic Control in Econometrics and Management Science (1980), North-Holland: North-Holland Amsterdam), 271-293 · Zbl 0461.90085
[10] Hammond, J. H., Solving Asymmetric Variational Inequality Problems and Systems of Equations with Generalized Network Programming Algorithms (1984), Dept. of Mathematics, M.I.T: Dept. of Mathematics, M.I.T Cambridge, MA, unpublished Ph.D. dissertation
[11] Harker, P. T., A variational inequality approach for the determination of oligopolistic market equilibrium, Mathematical Programming, 30, 105-111 (1984) · Zbl 0559.90015
[12] Harker, P. T., Alternatives models of spatial competition, Operations Research, 34, 410-425 (1986) · Zbl 0602.90018
[13] Harker, P. T., Accelerating the convergence of the diagonalization and projection algorithms for finite-dimensional inequalities, Mathematical Programming, 41, 29-59 (1988) · Zbl 0825.49019
[14] Ichiishi, T., Game Theory for Economic Analysis (1983), Academic Press: Academic Press New York · Zbl 0522.90104
[15] Kinderlehrer, D.; Stampacchia, G., An Introduction to Variational Inequalities and Their Applications (1980), Academic Press: Academic Press New York · Zbl 0457.35001
[16] Kyparisis, J., Sensitivity analysis framework for variational inequalities, Mathematical Programming, 36, 105-113 (1987)
[17] Lions, J. L.; Stampacchia, G., Variational inequalities, Communications on Pure and Applied Mathematics, 20, 493-519 (1967) · Zbl 0152.34601
[18] Lüthi, H. J., On the solution of variational inequalities by the ellipsoid method, Mathematics of Operations Research, 10, 515-522 (1985) · Zbl 0586.49016
[19] Marcotte, P., Network design problem with congestion effects: A case of bilevel programming, Mathematical Programming, 34, 142-162 (1986) · Zbl 0604.90053
[20] Moulin, H., Game Theory for the Social Sciences (1982), New York University Press: New York University Press New York · Zbl 0626.90095
[21] Pang, J. S.; Chan, D., Iterative methods for variational and complementary problems, Mathematical Programming, 24, 284-313 (1982) · Zbl 0499.90074
[22] Robinson, S. M., Strongly regular generalized equations, Mathematics of Operations Research, 5, 43-62 (1980) · Zbl 0437.90094
[23] Rosen, J. B., Existence and uniqueness of equilibrium points for concave \(n\)-person game, Econometrica, 33, 520-534 (1965) · Zbl 0142.17603
[24] Tobin, R. L., Sensitivity analysis for variational inequalities, Journal of Optimization Theory and Application, 48, 191-204 (1986) · Zbl 0557.49004
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