The parametric concept of equilibrium in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of the players into coalitions. In this situation, two extreme cases of this parеitioning correspond to the Pareto optimal outcome and the Nash equilibrium outcome, respectively. The parameter space of admissible perturbations in such a problem is formed by a set of additive matrices, with two arbitrary H¨older norms specified independently in the outcome and criterion spaces. The analysis of quasistability for a generalized optimal outcome under the perturbations of the linear payoff function coefficients is performed. The limiting level of such perturbations is found.