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. 
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     author = {Xeniya Grigorieva},
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     url = {http://geodesic.mathdoc.fr/item/CGTM_2011_4_a14/}
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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/

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