A Fixed Point Theorem for Discontinuous Functions

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.<P>This discussion paper has resulted in a publication in <A href="http://www.sciencedirect.com/science/article/pii/S0167637707000570"><I>Operations Research Letters</I></A>. (2008, vol. 36, issue 1, pp.89-93.)