Mathematical Control Theory

Solutions for a class of stochastic coalitional games

K. V. Grigor'eva

St. Petersburg State University, Faculty of Applied Mathematics and Control Processes

Abstract: In this paper one of classes of multistage stochastic games with various coalition structures is considered. The game under research is set on a tree graph. In each vertex $z$ of the tree the coalition structure of players is defined, along with the payoff function of coalitions, and the probability of transition to the following vertices of the tree depending on the situation realized in the game in vertex $z$. The new mathematical method is offered to building a solution of stochastic coalition games on the basis of calculation of the generalised PMS-vector as a solution of a coalition game. The offered method is illustrated by the 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