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A fixed point theorem for discontinuous functions

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Herings, Jean-Jacques [Universiteit Maastricht]

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.

Document type Article de périodique (Journal article)
Access type Accès interdit
Publication date 2008
Language Anglais
Journal information "Operations Research Letters" - Vol. 36, no. 1, p. 89-93 (2008)
Peer reviewed yes
Publisher Elsevier
issn 0167-6377
Publication status Publié
Affiliations Universiteit Maastricht - Department of Economics
UCL - EUEN/CORE - Center for operations research and econometrics
Keywords Fixed point ; Simplical subdivision ; Discontinuity ; Discontinuous games
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Bibliographic reference Herings, Jean-Jacques. A fixed point theorem for discontinuous functions. In: Operations Research Letters, Vol. 36, no. 1, p. 89-93 (2008)
Permanent URL http://hdl.handle.net/2078.1/28504