A Fixed Point Theorem for Discontinuous Functions

P.J.J. Herings*, G. van der Laan, A.J.J. Talman, Z. Yang

*Corresponding author for this work

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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.
Original languageEnglish
Pages (from-to)89-93
Number of pages4
JournalOperations Research Letters
Publication statusPublished - 1 Jan 2008

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