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.

In this paper we prove the following fixed point theorem. Consider a non-empty bounded polyhedron P and a function f from P to P such that for every x in P with f(x) not equal to x there is a ball in P around x such that the inner product of f(y)-y and f(z)-z is nonnegative for any two elements...

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...

In this paper we study cooperative games with limited cooperation possibilities, represented by an undirected cycle-free communication graph. Players in the game can cooperate if and only if they are connected in the graph, i.e. they can communicate with one another. We introduce a new...