In this paper we generalize the concept of coalitional games by allowing for any organizational structure within coalitions represented by a graphon the set of players ot the coalition. A, possibly empty, set of payoffvectors is assigned to any graph on every subset of players. Such a game will...

Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.