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A Fixed Point Theorem for Discontinuous Functions

Author

Listed:
  • Jean-Jacques Herings

    (Maastricht University)

  • Gerard van der Laan

    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Dolf Talman

    (Tilburg University)

  • Zaifu Yang

    (Yokohama National University)

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.)

Suggested Citation

  • Jean-Jacques Herings & Gerard van der Laan & Dolf Talman & Zaifu Yang, 2004. "A Fixed Point Theorem for Discontinuous Functions," Tinbergen Institute Discussion Papers 05-004/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20050004
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    References listed on IDEAS

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    1. Talman, A.J.J. & Yamamoto, Y., 1989. "A simplicial algorithm for stationary point problems on polytopes," Other publications TiSEM 0d6b2de0-17c0-4d5e-963f-5, Tilburg University, School of Economics and Management.
    2. Kim, Byung-Yeon & Korhonen, Iikka, 2005. "Equilibrium exchange rates in transition countries: Evidence from dynamic heterogeneous panel models," Economic Systems, Elsevier, vol. 29(2), pages 144-162, June.
    3. Herings, P.J.J., 1995. "Static and dynamic aspects of general disequilibrium theory," Other publications TiSEM 489c698d-c257-47a3-90bd-3, Tilburg University, School of Economics and Management.
    4. repec:zbw:bofitp:2003_011 is not listed on IDEAS
    5. Chihwa Kao & Min-Hsien Chiang, 1997. "On the Estimation and Inference of a Cointegrated Regression in Panel Data," Econometrics 9703001, University Library of Munich, Germany.
    6. repec:zbw:bofitp:2001_007 is not listed on IDEAS
    7. Dai, Y. & van der Laan, G. & Talman, A.J.J. & Yamamoto, Y., 1989. "A simplicial algorithm for the nonlinear stationary point problem on an unbounded polyhedron," Other publications TiSEM 82992276-1868-4b56-a937-0, Tilburg University, School of Economics and Management.
    8. Kao, Chihwa, 1999. "Spurious regression and residual-based tests for cointegration in panel data," Journal of Econometrics, Elsevier, vol. 90(1), pages 1-44, May.
    9. 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.
    10. Peter Pedroni, 2000. "Fully Modified OLS for Heterogeneous Cointegrated Panels," Department of Economics Working Papers 2000-03, Department of Economics, Williams College.
    11. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521266550.
    12. MacDonald, Ronald, 2000. "Concepts to Calculate Equilibrium Exchange Rates: An Overview," Discussion Paper Series 1: Economic Studies 2000,03, Deutsche Bundesbank.
    13. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
    14. P. Jean-Jacques Herings, 2000. "Two simple proofs of the feasibility of the linear tracing procedure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 485-490.
    15. Lommatzsch, Kirsten & Tober, Silke, 2004. "What is behind the real appreciation of the accession countries' currencies?: An investigation of the PPI-based real exchange rate," Economic Systems, Elsevier, vol. 28(4), pages 383-403, December.
    16. repec:zbw:bofitp:2002_015 is not listed on IDEAS
    17. International Monetary Fund, 2001. "Interpreting Real Exchange Rate Movements in Transition Countries," IMF Working Papers 2001/056, International Monetary Fund.
    18. Paul De Grauwe, 2003. "The Euro at Stake? The Monetary Union in an Enlarged Europe," CESifo Economic Studies, CESifo, vol. 49(1), pages 103-121.
    19. Ronald MacDonald & Cezary Wójcik, 2004. "Catching up: The role of demand, supply and regulated price effects on the real exchange rates of four accession countries," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 12(1), pages 153-179, March.
    20. Balazs Egert & Amina Lahrèche-Revil, 2003. "Estimating the Fundamental Equilibrium Exchange Rate of Central and Eastern European Countries; The EMU Enlargement Perspective," Working Papers 2003-05, CEPII research center.
    21. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    22. repec:zbw:bofitp:2003_014 is not listed on IDEAS
    23. Harris, Richard D. F. & Tzavalis, Elias, 1999. "Inference for unit roots in dynamic panels where the time dimension is fixed," Journal of Econometrics, Elsevier, vol. 91(2), pages 201-226, August.
    24. Virginie Coudert & Cécile Couharde, 2003. "Exchange Rate Regimes and Sustainable Parities for ceecs in the Run-up to emu Membership," Revue économique, Presses de Sciences-Po, vol. 54(5), pages 983-1012.
    25. A. J. J. Talman & Y. Yamamoto, 1989. "A Simplicial Algorithm for Stationary Point Problems on Polytopes," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 383-399, August.
    26. Jörg Rahn, 2003. "Bilateral Equilibrium Exchange Rates of the EU Accession Countries against the Euro," Quantitative Macroeconomics Working Papers 20306, Hamburg University, Department of Economics.
    27. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(1), pages 1-21, March.
    28. Gérard Debreu (ed.), 1996. "General Equilibrium Theory," Books, Edward Elgar Publishing, volume 0, number 548.
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    Citations

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    Cited by:

    1. Philippe Bich, 2007. "Nash equilibrium existence for some discontinuous games," Post-Print halshs-00188764, HAL.
    2. Philippe Bich, 2008. "An answer to a question of herings et al," Working Papers halshs-00265464, HAL.
    3. Philippe Bich, 2008. "An answer to a question of herings et al," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00265464, HAL.
    4. Zaifu Yang, 2008. "On the Solutions of Discrete Nonlinear Complementarity and Related Problems," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 976-990, November.
    5. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Cahiers de la Maison des Sciences Economiques b06066, Université Panthéon-Sorbonne (Paris 1).
    6. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Post-Print halshs-00119033, HAL.
    7. Takao Fujimoto, 2013. "Fixed Point Theorems for Discontinuous Maps on a Non-convex Domain," Metroeconomica, Wiley Blackwell, vol. 64(3), pages 547-572, July.
    8. Philippe Bich, 2008. "An answer to a question of herings et al," Post-Print halshs-00287667, HAL.

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    More about this item

    Keywords

    Fixed point; simplicial subdivision; discontinuity; equilibrium;
    All these keywords.

    JEL classification:

    • 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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