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.