Nash and Stackelberg solutions to general linear-quadratic two player difference games. I. Open-loop and feedback strategies

Raimo P. Hämäläinen

Kybernetika (1978)

  • Volume: 14, Issue: 1, page (38)-56
  • ISSN: 0023-5954

How to cite

top

Hämäläinen, Raimo P.. "Nash and Stackelberg solutions to general linear-quadratic two player difference games. I. Open-loop and feedback strategies." Kybernetika 14.1 (1978): (38)-56. <http://eudml.org/doc/28559>.

@article{Hämäläinen1978,
author = {Hämäläinen, Raimo P.},
journal = {Kybernetika},
language = {eng},
number = {1},
pages = {(38)-56},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Nash and Stackelberg solutions to general linear-quadratic two player difference games. I. Open-loop and feedback strategies},
url = {http://eudml.org/doc/28559},
volume = {14},
year = {1978},
}

TY - JOUR
AU - Hämäläinen, Raimo P.
TI - Nash and Stackelberg solutions to general linear-quadratic two player difference games. I. Open-loop and feedback strategies
JO - Kybernetika
PY - 1978
PB - Institute of Information Theory and Automation AS CR
VL - 14
IS - 1
SP - (38)
EP - 56
LA - eng
UR - http://eudml.org/doc/28559
ER -

References

top
  1. A. W. Starr Y., C. Ho, Nonzero-sum differential games, J. Optim. Theory. Applic. 3 (1969), 3, 184-206. (1969) Zbl0169.12303MR0249117
  2. A. W. Starr Y., C. Ho, Further properties of nonzero-sum differential games, J. Optim. Theory. Applic. 3 (1969), 4, 207-219. (1969) Zbl0169.12303MR0249118
  3. J. Marschak, Elements for a theory of teams, Management Science 1 (1955), 127-137. (1955) Zbl0995.90544MR0075521
  4. R. Radner, Team decision problems, Ann. Math. Statistics 33 (1962), 857-881. (1962) Zbl0217.57103MR0146937
  5. Y., C. Ho K., C. Chu, Team decision theory and information structures in optimal control problems - part I, IEEE Trans. Autom. Control AC-17 (1972), I, 15-22. (1972) MR0359875
  6. K., C. Chu, Team decision theory and information structures in optimal control problems - part II, IEEE Trans. Autom. Control AC-17 (1972), 1, 22-28. (1972) MR0359876
  7. R. Isaacs, Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, John Wiley and Sens, New York 1965. (1965) Zbl0125.38001MR0210469
  8. Y.-C. Ho A. E. Bryson Jr S. Baron, Differential games and optimal pursuit-evasion strategies, IEEE Trans Autom. Control AC-10 (1965), 4, 385-389. (1965) MR0184747
  9. J. H. Case, Toward a theory of many player differential games, SIAM J. Control 7 (1969), 2, 179-197. (1969) Zbl0176.39404MR0249111
  10. D. L. Lukes D. L. Russel, A global theory for linear-quadratic differential games, J. Math. Anal. Applic. 33 (1971), 96-123. (1971) MR0269324
  11. N. J. Krikelis Z. V. Rekasius, On the solution of the optimal linear control problems under conflict of interest, IEEE Trans. Autom. Control AC-16 (1971), 2, 140-147. (1971) MR0290810
  12. T. Basar, A counterexample in linear quadratic games: Existence of nonlinear Nash solutions, J. Optim. Theory. Applic. 14 (1974), 4, 425-430. (1974) MR0456552
  13. T. Basar, Nash strategies for M-person differential games with mixed information structures, Automatica 11 (1975), 5, 547-551. (1975) Zbl0318.90066MR0401190
  14. H. Stackelberg, Marktform und Gleichgewicht, Springer Verlag, Wien -Berlin 1934. (1934) 
  15. C. I. Chen J. B. Cruz, Jr, Stackelberg solution for two-person games with biased information patterns, IEEE Trans. Autom. Control. AC-17 (1972), 6, 791-798. (1972) 
  16. M. Simaan J. B. Cruz, Jr, On the Stackelberg strategy in nonzero-sum games, J. Optim. Theory. Applic. 11 (1973), 5, 533-555. (1973) MR0332207
  17. M. Simaan J. B. Cruz, Jr, Additional aspects of the Stackelberg strategy in nonzero-sum games, J. Optim. Theory. Applic. 11 (1973), 6, 613-627. (1973) MR0368809
  18. M. Simaan J. B. Cruz, Jr, Sampled-data Nash controls in non-zero-sum differential games, Int. J. Control 77 (1973), 6, 1201-1209. (1973) MR0327317
  19. M. Simaan J. B. Cruz, Jr, A Stackelberg solution for games with many players, IEEE Trans. Autom. Control. AC-18 (1973), 3, 322-324. (1973) MR0441373
  20. Y. Nishikawa H. Itakura H. Kitagawa, Nonzero-sum differential games with nonlinear dynamics, Institute of Electronics and Communication Engineers of Japan, Tokyo. Report NLP 71-18, 1972. (1972) 
  21. L. F. Pau, Differential games and a Nash equilibrium searching algorithm, SIAM J. Control 75 (1975), 4, 835-852. (1975) Zbl0269.90062MR0386720
  22. R. Mukundan W. B. Eisner, Linear feedback strategies in non-zero-sum differential games, Int. J. Systems Sci. 6 (1975), 6, 513-532. (1975) MR0371427
  23. J. Doležal, Necessary optimality conditions forN-player nonzero-sum multistage games, Kybernetika 12 (1976), 4, 268-295. (1976) MR0429152
  24. J. Doležal, Hierarchical solution concepts for static and multistage decision problems with two objectives, Kybernetika 12 (1976), 5, 363 - 385. (1976) MR0449468
  25. R. P. Hämäläinen, Nash and Stackelberg solutions to general linear-quadratic two-player difference games. Part II. Open-closed strategies, Kybernetika, 14 (1978), to appear. (1978) MR0479420

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.