# $Z$-equilibria in many-player stochastic differential games

Archivum Mathematicum (1993)

- Volume: 029, Issue: 3-4, page 123-133
- ISSN: 0044-8753

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topGaidov, Svatoslav. "$Z$-equilibria in many-player stochastic differential games." Archivum Mathematicum 029.3-4 (1993): 123-133. <http://eudml.org/doc/247449>.

@article{Gaidov1993,

abstract = {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.},

author = {Gaidov, Svatoslav},

journal = {Archivum Mathematicum},

keywords = {nonzero-sum game; many-player game; stochastic differential equation; linear-quadratic game; Bolza functional; cost-function; strategy; differential game; stochastic Itô equation},

language = {eng},

number = {3-4},

pages = {123-133},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {$Z$-equilibria in many-player stochastic differential games},

url = {http://eudml.org/doc/247449},

volume = {029},

year = {1993},

}

TY - JOUR

AU - Gaidov, Svatoslav

TI - $Z$-equilibria in many-player stochastic differential games

JO - Archivum Mathematicum

PY - 1993

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 029

IS - 3-4

SP - 123

EP - 133

AB - 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.

LA - eng

KW - nonzero-sum game; many-player game; stochastic differential equation; linear-quadratic game; Bolza functional; cost-function; strategy; differential game; stochastic Itô equation

UR - http://eudml.org/doc/247449

ER -

## References

top- Deterministic and Stochastic Optimal Control, Springer-Verlag, Berlin – Heidelberg – New York, 1975. (1975) MR0454768
- $Z$-Equilibrium in Stochastic Differential Games, (in Russian), In: Many Player Differential Games, Centre of Mathematics, Technical University, Rouse, Bulgaria (1984), 53-63.
- Basic Optimal Strategies in Stochastic Differential Games, C. R. Acad. Bulgare Sci. 37 (1984), 457-460. (1984) Zbl0546.93065MR0758144
- Pareto-Optimality in Stochastic Differential Games, Problems of Control and Information Theory 15 (1986), 439-450. (1986) Zbl0631.90105MR0887278
- Nash Equilibrium in Stochastic Differential Games, Computers and Mathematics with Applications 12A (1986), 761-768. (1986) Zbl0641.93056MR0855775
- Guaranteeing Strategies in Many Player Stochastic Differential Games, In: Mathematics and Educatin in Mathematics, Proceedings of 15th Spring Conference of UBM (1986), 379-383. (1986) MR0872944
- Automatic Control, (in Russian), Nauka, Moscow, 1978. (1978) MR1222869
- Introduction into Many Player Differential Games, (in Russian), Sovetskoe Radio (1980), Moscow. (1980)

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