| Article ID: | iaor2009594 |
| Country: | Netherlands |
| Volume: | 36 |
| Issue: | 1 |
| Start Page Number: | 89 |
| End Page Number: | 93 |
| Publication Date: | Jan 2008 |
| Journal: | Operations Research Letters |
| Authors: | Talman Dolf, Yang Zaifu, Laan Gerard van der, Herings P. Jean-Jacques |
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.