A Fixed Point Theorem for Discontinuous Functions
AbstractAny 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.)
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-004/1.
Date of creation: 11 Jan 2004
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Fixed point; simplicial subdivision; discontinuity; equilibrium;
Other versions of this item:
- HERINGS, P. Jean-Jacques & van der LAAN, Gerard & TALMAN, Dolf & YANG, Zaifu, . "A fixed point theorem for discontinuous functions," CORE Discussion Papers RP -2154, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Herings,Jean-Jacques & Laan,Gerard,van der & Talman,Dolf & Yang,Zaifu, 2005. "A Fixed Point Theorem for Discontinuous Functions," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Herings, P.J.J. & Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2008. "A fixed point theorem for discontinuous functions," Open Access publications from Tilburg University urn:nbn:nl:ui:12-357915, Tilburg University.
- Herings, P.J.J. & Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2005. "A Fixed Point Theorem for Discontinuous Functions," Discussion Paper 2005-4, Tilburg University, Center for Economic Research.
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
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- repec:hal:cesptp:halshs-00265464 is not listed on IDEAS
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