Geodesic
Solutions for a~class stochastic coalitional games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 1, pp. 47-66

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In the paper one of classes of multistage stochastic games with various coalition structures is considered. Game researched here is set on the tree graph where in each vertex $z$ coalition structures of players, function of a payoff of coalitions and probability of transition in following vertexes depending on a situation realised in game, set in vertex $z$ is defined. A new mathematical method of the decision of stochastic coalition games on the basis of calculation of the generalised PMS-vector as decisions of coalition games is offered. The offered method is illustrated by example of three-step stochastic game of three persons with variable coalition structure.
Keywords: optimization, multistage games, stochastic games, Nash equilibrium, PMS-vector. 
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     author = {Kseniya V. Grigorieva},
     title = {Solutions for a~class stochastic coalitional games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {47--66},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2010_2_1_a2/}
}
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Kseniya V. Grigorieva. Solutions for a~class stochastic coalitional games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 1, pp. 47-66. http://geodesic.mathdoc.fr/item/MGTA_2010_2_1_a2/