The regular convex cooperative linear quadratic control problem

In this note we consider the cooperative linear quadratic control problem. That is, the problem where a number of players, all facing a (different) linear quadratic control problem, decide to cooperate in order to optimize their performance. It is well-known, when the performance criteria are positive definite, how one can determine the set of Pareto efficient equilibria for these games. In this note we generalize this result for indefinite criteria.