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A fixed point theorem for discontinuous functions |
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| Authors: | P Jean-Jacques Herings Gerard van der Laan |
| Institution: | a Department of Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands b Department of Econometrics and Tinbergen Institute, Vrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands c Department of Econometrics & Operations Research and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands d Faculty of Business Administration, Yokohama National University, Yokohama 240-8501, Japan |
| Abstract: | 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. |
| Keywords: | 47H10 65K10 91A10 |
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