A note on a class of equilibrium problems with equilibrium constraints

Jiří V. Outrata

Kybernetika (2004)

  • Volume: 40, Issue: 5, page [585]-594
  • ISSN: 0023-5954

Abstract

top
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.

How to cite

top

Outrata, Jiří V.. "A note on a class of equilibrium problems with equilibrium constraints." Kybernetika 40.5 (2004): [585]-594. <http://eudml.org/doc/33721>.

@article{Outrata2004,
abstract = {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.},
author = {Outrata, Jiří V.},
journal = {Kybernetika},
keywords = {hierarchical game; Nash equilibrium; stationarity conditions; hierarchical game; Nash equilibrium; stationarity condition},
language = {eng},
number = {5},
pages = {[585]-594},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A note on a class of equilibrium problems with equilibrium constraints},
url = {http://eudml.org/doc/33721},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Outrata, Jiří V.
TI - A note on a class of equilibrium problems with equilibrium constraints
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 5
SP - [585]
EP - 594
AB - 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.
LA - eng
KW - hierarchical game; Nash equilibrium; stationarity conditions; hierarchical game; Nash equilibrium; stationarity condition
UR - http://eudml.org/doc/33721
ER -

References

top
  1. J.-P.Aubin, Optima and Equilibria, Springer–Verlag, Berlin 1993 Zbl1074.91579MR1217485
  2. Clarke F. H., Optimization and Nonsmooth Analysis, Wiley, New York 1983 Zbl0696.49002MR0709590
  3. Dontchev A. D., Rockafellar R. T., 10.1137/S1052623495284029, SIAM J. Optim. 7 (1996), 1087–1105 (1996) MR1416530DOI10.1137/S1052623495284029
  4. Eaves B. C., 10.1007/BF01584975, Math. Programming 3 (1972), 1–22 (1972) Zbl0276.55004MR0303953DOI10.1007/BF01584975
  5. Fang S. C., Peterson E. L., 10.1007/BF00935344, J. Optim. Theory Appl. 38 (1982), 363–383 (1982) Zbl0471.49007MR0686212DOI10.1007/BF00935344
  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 Zbl0732.90075
  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 
  8. Luo Z.-Q., Pang J.-S., Ralph D., Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge 1996 Zbl1139.90003MR1419501
  9. Mordukhovich B. S., Approximation Methods in Problems of Optimization and Control (in Russian), Nauka, Moscow 1988 MR0945143
  10. Mordukhovich B. S., 10.1006/jmaa.1994.1144, J. Math. Anal. Appl. 183 (1994), 250–288 (1994) Zbl0807.49016MR1273445DOI10.1006/jmaa.1994.1144
  11. Mordukhovich B. S., Optimization and Equilibrium Problems with Equilibrium Constraints, Preprint 2003. To appear in Omega Zbl1161.49015MR2473868
  12. Mordukhovich B. S., 10.1080/1055678042000218966, Optimization Methods & Software 19 (2004), 5 MR2095348DOI10.1080/1055678042000218966
  13. Murphy F. H., Sherali H. D., Soyster A. L., 10.1007/BF01585096, Math. Programming 24 (1982), 92–106 (1982) Zbl0486.90015MR0667941DOI10.1007/BF01585096
  14. Nash J. F., 10.2307/1969529, Ann. of Math. 54 (1951), 286–295 (1951) Zbl0045.08202MR0043432DOI10.2307/1969529
  15. Outrata J. V., 10.1287/moor.24.3.627, Math. Oper. Res. 24 (1999), 627–644 (1999) Zbl1039.90088MR1854246DOI10.1287/moor.24.3.627
  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 MR1818625
  17. Outrata J. V., Zowe J., 10.1007/BF01585759, Math. Programming 68 (1995), 105–130 (1995) Zbl0835.90093MR1312107DOI10.1007/BF01585759
  18. Outrata J. V., Kočvara, M., Zowe J., Nonsmooth Approach to Optimization Problems with Equilibrium Constraints, Kluwer, Dordrecht 1998 Zbl0947.90093MR1641213
  19. Robinson S. M., 10.1007/BFb0120929, Math. Programming Stud. 14 (1981), 206–214 (1981) Zbl0449.90090MR0600130DOI10.1007/BFb0120929
  20. Scholtes S., On the existence and computation of EPEC solutions, A talk given at the ICCP Conference in Cambridge, 2002 
  21. Scheel H., Scholtes S., 10.1287/moor.25.1.1.15213, Math. Oper. Res. 25 (2000), 1–22 MR1854317DOI10.1287/moor.25.1.1.15213
  22. Ye J. J., Ye X. Y., 10.1287/moor.22.4.977, Math. Oper. Res. 22 (1997), 977–997 (1997) Zbl1088.90042MR1484692DOI10.1287/moor.22.4.977

Citations in EuDML Documents

top
  1. René Henrion, Werner Römisch, On M -stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling
  2. René Henrion, Jiří Outrata, Thomas Surowiec, Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market
  3. René Henrion, Jiří Outrata, Thomas Surowiec, Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market
  4. Truong Q. Bao, Boris S. Mordukhovich, Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.