On Stability of an Optimal Situation in a Finite Cooperative Game with a Parametric Concept of Equilibrium (from Lexicographic Optimality to Nash Equilibrium).

A parametric concept of equilibrium (principle of optimality) in a finite cooperative game in normal form of several players is introduced. This concept is defined by means of the partition of players into coalitions. Lexicographically optimal situation and Nash equilibrium situation correspond to two special cases of this partition. The quantitative analysis of stability of an optimal situation for the independent perturbations of players' payoff functions is performed. The maximum level of such perturbations which save the optimality of a situation is found. Mathematics Subject Classification 2000: 90C05, 90C10, 90C29, 90C31