Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2004-01-11 Number: 05-004/1 Author-Name: Jean-Jacques Herings Author-Email: P.Herings@algec.unimaas.nl Author-Workplace-Name: Maastricht University Author-Name: Gerard van der Laan Author-Email: glaan@feweb.vu.nl Author-Workplace-Name: Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam Author-Name: Dolf Talman Author-Email: talman@uvt.nl Author-Workplace-Name: Tilburg University Author-Name: Zaifu Yang Author-Email: zyang@business.ynu.ac.jp Author-Workplace-Name: Yokohama National University Title: A Fixed Point Theorem for Discontinuous Functions 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.

This discussion paper has resulted in a publication in Operations Research Letters. (2008, vol. 36, issue 1, pp.89-93.) Classification-JEL: C62; C63 Keywords: Fixed point; simplicial subdivision; discontinuity; equilibrium File-Url: https://papers.tinbergen.nl/05004.pdf File-Format: application/pdf File-Size: 487755 bytes Handle: RePEc:tin:wpaper:20050004