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.

Key Features:Offers many new fixed-point theorems together with mathematical structures that can be utilized to describe many general economic equilibrium settings and views of the worldTreats methods for fixed-point and equilibrium arguments under the framework of "homology theory", so that the...