Geodesic
Solution for a Class of Stochastic Coalitional Games
Contributions to game theory and management, Tome 3 (2010), pp. 144-161

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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 probability distribution over the coalitional structures of each stage game depends on the initial stage game $G$ and the $n$-tuple of strategies realized in this game. 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_2010_3_a12,
     author = {Xeniya Grigorieva},
     title = {Solution for a {Class} of {Stochastic} {Coalitional} {Games}},
     journal = {Contributions to game theory and management},
     pages = {144--161},
     publisher = {mathdoc},
     volume = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2010_3_a12/}
}
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Xeniya Grigorieva. Solution for a Class of Stochastic Coalitional Games. Contributions to game theory and management, Tome 3 (2010), pp. 144-161. http://geodesic.mathdoc.fr/item/CGTM_2010_3_a12/