Minimum norm solutions for cooperative games

We show that to each linear solution that has the inessential game property, there is an inner product on the space of games such that the solution to each game is the best additive approximation of the game (w.r.t. the norm derived from this inner product). If the space of games has an inner product, then the function that to each game assigns the best additive approximation of this game (w.r.t. to the norm derived from this inner product) is a linear solution that has the inessential game property. Both claims remain valid also if solutions are required to be efficient. JEL Classification: C78