The asymptotic nucleolus of large monopolistic games

Abstract

We study the asymptotic nucleolus of large differentiable monopolistic games. We show that if v is a monopolistic game which is a composition of a non-decreasing concave and differentiable function with a vector of measures, then v has an asymptotic nucleolus. We also provide an explicit formula for the asymptotic nucleolus of v and show that it coincides with the center of symmetry of the subset of the core of v in which all the monopolists obtain the same payoff. We apply this result to large monopolistic market games to obtain a relationship between the asymptotic nucleolus of the game and the competitive payoff distributions of the market.