Geodesic
Stochastic Coalitional Games with Constant Matrix of Transition Probabilties
Contributions to game theory and management, Tome 4 (2011), pp. 199-212

Voir la notice de l'article provenant de la source Math-Net.Ru

The stochastic game $\Gamma$ under consideration is repetition of the same stage game $G$ which is played on each stage with different coalitional partitions. The transition probabilities over the coalitional structures of stage game depends on the initial stage game $G$ in game $\Gamma$. The payoffs in stage games (which is a simultaneous game with a given coalitional structure) are computed as components of the generalized PMS-vector (see (Grigorieva and Mamkina, 2009), (Petrosjan and Mamkina, 2006)). The total payoff of each player in game $\Gamma$ is equal to the mathematical expectation of payoffs in different stage games $G$ (mathematical expectation of the components of PMS-vector). The concept of solution for such class of stochastic game is proposed and the existence of this solution is proved. The theory is illustrated by 3-person 3-stage stochastic game with changing coalitional structure.
Keywords: stochastic games, coalitional partition, Nash equilibrium, Shapley value, PMS-vector. 
@article{CGTM_2011_4_a14,
     author = {Xeniya Grigorieva},
     title = {Stochastic {Coalitional} {Games} with {Constant} {Matrix} of {Transition} {Probabilties}},
     journal = {Contributions to game theory and management},
     pages = {199--212},
     publisher = {mathdoc},
     volume = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2011_4_a14/}
}
TY  - JOUR
AU  - Xeniya Grigorieva
TI  - Stochastic Coalitional Games with Constant Matrix of Transition Probabilties
JO  - Contributions to game theory and management
PY  - 2011
SP  - 199
EP  - 212
VL  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2011_4_a14/
LA  - en
ID  - CGTM_2011_4_a14
ER  - 
%0 Journal Article
%A Xeniya Grigorieva
%T Stochastic Coalitional Games with Constant Matrix of Transition Probabilties
%J Contributions to game theory and management
%D 2011
%P 199-212
%V 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2011_4_a14/
%G en
%F CGTM_2011_4_a14
Xeniya Grigorieva. Stochastic Coalitional Games with Constant Matrix of Transition Probabilties. Contributions to game theory and management, Tome 4 (2011), pp. 199-212. http://geodesic.mathdoc.fr/item/CGTM_2011_4_a14/