The kernel of a patent licensing game: The optimal number of licensees

This paper considers general bargaining outcomes under coalition structures formed by an external patent holder and firms in oligopoly markets, where a coalition structure is eventually determined by the patent holder. Our main proposition is that, for each permissible coalition structure, the kernel is a singleton; thus, the number of licensees that maximizes the patent holder's revenue can be determined with the kernel. Specifying the upper and lower bounds of the kernel for each coalition structure, we also provide the sufficient conditions for the integer that maximizes the licensees' total surplus to be the optimal number of licensees for the patent holder. The numerical comparison of the bargaining outcomes to those obtained by non-cooperative licensing by means of fee through take-it-or-leave-it offers is provided for a cost-reducing innovation in a linear Cournot market. Regardless of the ways of licensing, the producer surplus is maximized when the magnitude of cost reduction is large.