Solution set in a special case of generalized Nash equilibrium games

Josef Cach

Kybernetika (2001)

  • Volume: 37, Issue: 1, page [21]-37
  • ISSN: 0023-5954

Abstract

top
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.

How to cite

top

Cach, Josef. "Solution set in a special case of generalized Nash equilibrium games." Kybernetika 37.1 (2001): [21]-37. <http://eudml.org/doc/33514>.

@article{Cach2001,
abstract = {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.},
author = {Cach, Josef},
journal = {Kybernetika},
keywords = {generalized Nash equilibrium problem; Cournot oligopoly problem; generalized Nash equilibrium problem; Cournot oligopoly problem},
language = {eng},
number = {1},
pages = {[21]-37},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Solution set in a special case of generalized Nash equilibrium games},
url = {http://eudml.org/doc/33514},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Cach, Josef
TI - Solution set in a special case of generalized Nash equilibrium games
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 1
SP - [21]
EP - 37
AB - 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.
LA - eng
KW - generalized Nash equilibrium problem; Cournot oligopoly problem; generalized Nash equilibrium problem; Cournot oligopoly problem
UR - http://eudml.org/doc/33514
ER -

References

top
  1. Arrow K., Debreu G., 10.2307/1907353, Econometrica 22 (1954), 265–290 (1954) MR0077069DOI10.2307/1907353
  2. Baiocchi C., Capelo A., Variational and Quasi-Variational Inequalities, Wiley, New York 1984 MR0745619
  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., 10.1287/moor.7.2.211, Math. Oper. Res. 7 (1982), 211–222 (1982) MR0665558DOI10.1287/moor.7.2.211
  5. Debreu G., 10.1073/pnas.38.10.886, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 886–893 (1952) Zbl0047.38804MR0050251DOI10.1073/pnas.38.10.886
  6. Harker P. T., 10.1007/BF02591802, Math. Programming 30 (1984), 105–111 (1984) Zbl0559.90015MR0755118DOI10.1007/BF02591802
  7. Harker P. T., 10.1016/0377-2217(91)90325-P, European J. Oper. Res. 54 (1991), 81–94 (1991) Zbl0754.90070DOI10.1016/0377-2217(91)90325-P
  8. Harker P. T., Pang J.-S., 10.1007/BF01582255, Math. Programming 60 (1990), 161–220 (1990) MR1073707DOI10.1007/BF01582255
  9. Ichiishi T., Game Theory for Economic Analysis, Academic Press, New York 1983 Zbl0522.90104MR0700688
  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 (19 S) MR0513202
  11. Murphy F. H., Sherali H. D., Soyster A. L., 10.1007/BF01585096, Math. Programming 24 (1982), 92–106 (1982) Zbl0486.90015MR0667941DOI10.1007/BF01585096
  12. Nash J., 10.2307/1969529, Ann. of Math. 54 (1951), 286–295 (1951) Zbl0045.08202MR0043432DOI10.2307/1969529
  13. Outrata J. V., Kočvara M., Zowe J., Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results, Kluwer, Dordrecht 1998 Zbl0947.90093MR1641213
  14. Outrata J. V., Zowe J., 10.1007/BF01585759, Math. Programming 68 (1995), 105–130 (1995) Zbl0835.90093MR1312107DOI10.1007/BF01585759
  15. Rosen J. B., 10.2307/1911749, Econometrica 33 (1965), 520–534 (1965) Zbl0142.17603MR0194210DOI10.2307/1911749

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.