A fixed point theorem for discontinuous functions

Authors :: P. Jean-Jacques Herings
Gerard van der Laan
Dolf Talman
Zaifu Yang
Research Group: Economics
Research Group: Operations Research
Econometrics and Operations Research
Microeconomics & Public Economics
Externe publicaties SBE
RS: GSBE ETBC
Source :: Herings, P J J, van der Laan, G, Talman, A J J & Yang, Z 2008, ' A fixed point theorem for discontinuous functions ', Operations Research Letters, vol. 36, pp. 89-93 . https://doi.org/10.1016/j.orl.2007.03.008, Operations Research Letters, 36(1), 89-93. Elsevier, Operations Research Letters, 36, 89-93. Elsevier Science, Tilburg University-PURE, Operations Research Letters, 36, 89-93. Elsevier
Publication Year :: 2008
Publisher :: Elsevier, 2008.
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.)