Morenets V. Game problems with a fuzzy set of agents

The dissertation is devoted to research of actual problems in the game theory in terms of fuzzy information and the methods developing for solving game problems with fuzzy structure. The concept of the solution of the problem of "maximizing" function on a type-2 fuzzy set (T2 FS) is proposed. The choice of "feasible" alternatives from T2 FS is solved. The basic principles of optimality in non-cooperative games with fuzzy sets of players are developed. The follows notions are generalized: the Nash’s equilibrium, the altruistic Berg’s equilibrium and the Berg’s equilibrium with a fuzzy coalitions of the "sympathetic" players. Methods of finding these equilibrium with the maximum degree of feasibility and the degree of unfeasibility, not exceeding a given threshold. The concept of the C-core and the Shapley value for cooperative games with the fuzzy set of feasible coalitions is generalized. Their properties are investigated and methods of their finding are developed.