Title:
|
A note on a class of equilibrium problems with equilibrium constraints (English) |
Author:
|
Outrata, Jiří V. |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
40 |
Issue:
|
5 |
Year:
|
2004 |
Pages:
|
[585]-594 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
The paper concerns a two-level hierarchical game, where the players on each level behave noncooperatively. In this way one can model eg an oligopolistic market with several large and several small firms. We derive two types of necessary conditions for a solution of this game and discuss briefly the possibilities of its computation. (English) |
Keyword:
|
hierarchical game |
Keyword:
|
Nash equilibrium |
Keyword:
|
stationarity conditions |
MSC:
|
49J40 |
MSC:
|
49J52 |
MSC:
|
49K40 |
MSC:
|
65K10 |
MSC:
|
90C30 |
MSC:
|
90C47 |
MSC:
|
91A65 |
MSC:
|
91B24 |
idZBL:
|
Zbl 1249.49017 |
idMR:
|
MR2120998 |
. |
Date available:
|
2009-09-24T20:04:02Z |
Last updated:
|
2015-03-23 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135618 |
. |
Reference:
|
[1] J.-P.Aubin: Optima and Equilibria.Springer–Verlag, Berlin 1993 Zbl 1074.91579, MR 1217485 |
Reference:
|
[2] Clarke F. H.: Optimization and Nonsmooth Analysis.Wiley, New York 1983 Zbl 0696.49002, MR 0709590 |
Reference:
|
[3] Dontchev A. D., Rockafellar R. T.: Characterization of strong regularity for variational inequalities over polyhedral convex sets.SIAM J. Optim. 7 (1996), 1087–1105 MR 1416530, 10.1137/S1052623495284029 |
Reference:
|
[4] Eaves B. C.: Homotopies for computation of fixed points.Math. Programming 3 (1972), 1–22 Zbl 0276.55004, MR 0303953, 10.1007/BF01584975 |
Reference:
|
[5] Fang S. C., Peterson E. L.: Generalized variational inequalities.J. Optim. Theory Appl. 38 (1982), 363–383 Zbl 0471.49007, MR 0686212, 10.1007/BF00935344 |
Reference:
|
[6] Harker P. T., Choi S. C.: A Penalty Function Approach for Mathematical Programs with Variational Inequality Constraints.WP 87-08-08, University of Pennsylvania Zbl 0732.90075 |
Reference:
|
[7] Hu X., Ralph D., Ralph E. K., Bardsley, P., Ferris M. C.: The Effect of Transmission Capacities on Competition in Deregulated Electricity Markets.Preprint 2002 |
Reference:
|
[8] Luo Z.-Q., Pang J.-S., Ralph D.: Mathematical Programs with Equilibrium Constraints.Cambridge University Press, Cambridge 1996 Zbl 1139.90003, MR 1419501 |
Reference:
|
[9] Mordukhovich B. S.: Approximation Methods in Problems of Optimization and Control (in Russian).Nauka, Moscow 1988 MR 0945143 |
Reference:
|
[10] Mordukhovich B. S.: Generalized differential calculus for nonsmooth and set-valued mappings.J. Math. Anal. Appl. 183 (1994), 250–288 Zbl 0807.49016, MR 1273445, 10.1006/jmaa.1994.1144 |
Reference:
|
[11] Mordukhovich B. S.: Optimization and Equilibrium Problems with Equilibrium Constraints.Preprint 2003. To appear in Omega Zbl 1161.49015, MR 2473868 |
Reference:
|
[12] Mordukhovich B. S.: Equlibrium problems with equilibrium constraints via multiobjective optimization.Optimization Methods & Software 19 (2004), 5 MR 2095348, 10.1080/1055678042000218966 |
Reference:
|
[13] 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, MR 0667941, 10.1007/BF01585096 |
Reference:
|
[14] Nash J. F.: Non-cooperative games.Ann. of Math. 54 (1951), 286–295 Zbl 0045.08202, MR 0043432, 10.2307/1969529 |
Reference:
|
[15] Outrata J. V.: Optimality conditions for a class of mathematical programs with equilibrium constraints.Math. Oper. Res. 24 (1999), 627–644 Zbl 1039.90088, MR 1854246, 10.1287/moor.24.3.627 |
Reference:
|
[16] Outrata J. V.: On constrained qualifications for mathematical programs with mixed complementarity constraints.In: Complementarity: Applications, Algorithms and Extensions (M. C. Ferris, O. L. Mangasarian and J.-S. Pang, eds.), Kluwer, Dordrecht 2001, pp. 253–272 MR 1818625 |
Reference:
|
[17] Outrata J. V., Zowe J.: A numerical approach to optimization problems with variational inequality constraints.Math. Programming 68 (1995), 105–130 Zbl 0835.90093, MR 1312107, 10.1007/BF01585759 |
Reference:
|
[18] Outrata J. V., Kočvara, M., Zowe J.: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints.Kluwer, Dordrecht 1998 Zbl 0947.90093, MR 1641213 |
Reference:
|
[19] Robinson S. M.: Some continuity properties of polyhedral multifunctions.Math. Programming Stud. 14 (1981), 206–214 Zbl 0449.90090, MR 0600130, 10.1007/BFb0120929 |
Reference:
|
[20] Scholtes S.: On the existence and computation of EPEC solutions.A talk given at the ICCP Conference in Cambridge, 2002 |
Reference:
|
[21] Scheel H., Scholtes S.: Mathematical programs with equilibrium constraints: Stationarity, optimality and sensitivity.Math. Oper. Res. 25 (2000), 1–22 MR 1854317, 10.1287/moor.25.1.1.15213 |
Reference:
|
[22] Ye J. J., Ye X. Y.: Necessary optimality conditions for optimization problems with variational inequality constraints.Math. Oper. Res. 22 (1997), 977–997 Zbl 1088.90042, MR 1484692, 10.1287/moor.22.4.977 |
. |