A Fixed Point Theorem for Discontinuous Functions

P. Jean-Jacques Herings, Gerard van der Laan, Adolphus Talman and Zaifu Yang

No 05-004/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.)

Keywords: Fixed point; simplicial subdivision; discontinuity; equilibrium (search for similar items in EconPapers)
JEL-codes: C62 C63 (search for similar items in EconPapers)
Date: 2004-01-11
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Related works:
Working Paper: A fixed point theorem for discontinuous functions (2009)
Working Paper: A fixed point theorem for discontinuous functions (2008)
Working Paper: A Fixed Point Theorem for Discontinuous Functions (2005)
Working Paper: A Fixed Point Theorem for Discontinuous Functions (2005)
Working Paper: A fixed point theorem for discontinuous functions (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20050004

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