On the relation between Nash bargaining solution and the weighting method

A set of n-person convex bargaining problems is considered where the feasible payoff set is the same, but the disagreement payoff vector is −αr with a given positive vector r and positive real parameter α. It is shown as α→∞, the limit of the Nash solution is an optimal solution obtained by the weighting method where the weights are reciprocals of the components of vector r. The limit of the Nash solution is axiomatized in the multicriteria decision context and is determined as the unique minimum of a convex programming problem.