Stability and accuracy functions in a coalition game with bans, linear payoffs and antagonistic strategies

A coalition game with a finite number of players in which initial coefficients of linear payoff functions are subject to perturbations is considered. For any efficient solution which may appear in the game, appropriate measures of the quality are introduced. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multiobjective combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied. Maximum norms of perturbations for which an efficient in sense of equilibrium solution preserves the property of being efficient are calculated.