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,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., 2005. "A Fixed Point Theorem for Discontinuous Functions," Discussion Paper 2005-4, Tilburg University, Center for Economic Research.
- 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, 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.
- 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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- P. Jean-Jacques Herings, 2000.
"Two simple proofs of the feasibility of the linear tracing procedure,"
Springer, vol. 15(2), pages 485-490.
- Herings, P.J.J., 1997. "Two Simple Proofs of the Feasibility of the Linear Tracing Procedure," Discussion Paper 1997-77, Tilburg University, Center for Economic Research.
- Shoven,John B. & Whalley,John, 1992.
"Applying General Equilibrium,"
Cambridge University Press, number 9780521319867.
- Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
- Carolyn Pitchik, 1981. "Equilibria of a Two-Person Non-Zero Sum Noisy Game of Timing," Cowles Foundation Discussion Papers 579, Cowles Foundation for Research in Economics, Yale University.
- Talman, A.J.J. & Yamamoto, Y., 1989. "A simplicial algorithm for stationary point problems on polytopes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153111, Tilburg University.
- Philippe Bich, 2008. "An answer to a question of herings et al," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00265464, HAL.
- Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Cahiers de la Maison des Sciences Economiques b06066, Université Panthéon-Sorbonne (Paris 1).
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