For a quarter century, a top priority in transportation economic theory has been to develop models of rush-hour traffic dynamics that incorporate traffic jams (hypercongestion). The difficulty has been that "proper" models result in mathematical intractabilty, while none of the proposed...

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.