von Neumann-Morgenstern stable sets of a patent licensing game: The existence proof

This paper provides the existence proof for stable sets of a game which may have empty cores. Given the number of licensees of a patented technology which is determined by the patent holder without any production facilities, a game with a coalition structure is formulated with the outcome expected in the subsequent market competition where any cartels are prohibited. Although the core is non-empty if and only if the grand coalition is formed with a condition, we provide, for each permissible coalition structure, the sufficient condition(s) for the existence of von Neumann-Morgenstern stable sets of the game. Under symmetric imputations, there exist stable sets for any permissible coalition structures, and each of those is completely characterized.