| Title:
|
$Z$-equilibria in many-player stochastic differential games (English) |
| Author:
|
Gaidov, Svatoslav |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
123-133 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper $N$-person nonzero-sum games are considered. The dynamics is described by Ito stochastic differential equations. The cost-functions are conditional expectations of functionals of Bolza type with respect to the initial situation. The notion of $Z$-equilibrium is introduced in many-player stochastic differential games. Some properties of $Z$-equilibria are analyzed. Sufficient conditions are established guaranteeing the $Z$-equilibrium for the strategies of the players. In a particular case of a linear-quadratic game the $Z$-equilibrium strategies are found in an explicit form. (English) |
| Keyword:
|
nonzero-sum game |
| Keyword:
|
many-player game |
| Keyword:
|
stochastic differential equation |
| Keyword:
|
linear-quadratic game |
| Keyword:
|
Bolza functional |
| Keyword:
|
cost-function |
| Keyword:
|
strategy |
| MSC:
|
90D15 |
| MSC:
|
91A10 |
| MSC:
|
91A60 |
| MSC:
|
93E05 |
| idZBL:
|
Zbl 0816.93077 |
| idMR:
|
MR1263113 |
| . |
| Date available:
|
2008-06-06T21:24:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107474 |
| . |
| Reference:
|
[1] Fleming, W. H., Rishel, R. W.: Deterministic and Stochastic Optimal Control.Springer-Verlag, Berlin – Heidelberg – New York, 1975. MR 0454768 |
| Reference:
|
[2] Gaidov, S. D.: $Z$-Equilibrium in Stochastic Differential Games.(in Russian), In: Many Player Differential Games, Centre of Mathematics, Technical University, Rouse, Bulgaria (1984), 53-63. |
| Reference:
|
[3] Gaidov, S. D.: Basic Optimal Strategies in Stochastic Differential Games.C. R. Acad. Bulgare Sci. 37 (1984), 457-460. Zbl 0546.93065, MR 0758144 |
| Reference:
|
[4] Gaidov, S. D.: Pareto-Optimality in Stochastic Differential Games.Problems of Control and Information Theory 15 (1986), 439-450. Zbl 0631.90105, MR 0887278 |
| Reference:
|
[5] Gaidov, S. D.: Nash Equilibrium in Stochastic Differential Games.Computers and Mathematics with Applications 12A (1986), 761-768. Zbl 0641.93056, MR 0855775 |
| Reference:
|
[6] Gaidov, S. D.: Guaranteeing Strategies in Many Player Stochastic Differential Games.In: Mathematics and Educatin in Mathematics, Proceedings of 15th Spring Conference of UBM (1986), 379-383. MR 0872944 |
| Reference:
|
[7] Roitenberg, Y. N.: Automatic Control.(in Russian), Nauka, Moscow, 1978. MR 1222869 |
| Reference:
|
[8] Vaisbord, I. M., Zhukovskii, V. I.: Introduction into Many Player Differential Games.(in Russian), Sovetskoe Radio (1980), Moscow. |
| . |
