The asymptotic kernel in TU production market games with symmetric big players and a uniform ocean of small players

We apply the mixed measure space model of players to the analysis of smooth oligopolies with two types of players. Following Kannai (1966) and others, we use the asymptotic approach to obtain the structure of the asymptotic kernel for smooth Transferable Utility production market games with symmetric big players and a uniform ocean of small players. We show that in the case of a duopoly, the asymptotic kernel is a nondegenerate interval that strictly contains the asymptotic nucleolus, which in turn coincides with the unique Transferable Utility Competitive Equilibrium being the upper end-point of the interval (from the point of view of the uniform ocean).