Solutions for a class stochastic coalitional games

Kseniya V. Grigorieva

Saint-Petersburh State University, Saint-Petersburg

Abstract: 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.

UDC: 519.83
BBK: 22.18