Measure of stability for a finite cooperative game with a generalized concept of equilibrium

We consider a finite cooperative game in the normal form with a parametric principle of optimality (the generalized concept of equilibrium). This principle is defined by the partition of the players into coalitions. In this situation, two extreme cases of this partition correspond to the lexicographically optimal situation and the Nash equilibrium situation, respectively. The analysis of stability for a set of generalized equilibrium situations under the perturbations of the coefficients of the linear payoff functions is performed. Upper and lower bounds of the stability radius in the $l_\infty$-metric are obtained. We show that the lower bound of the stability radius is accessible.