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A constructive proof of Ky Fan’s coincidence theorem

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Abstract

We present a constructive proof for the well-known Ky Fan’s coincidence theorem through a simplicial algorithm. In a finite number of steps the algorithm generates a simplex containing an approximate coincidence point. In the limit, when the mesh size converges to zero, the sequence of approximations converges to a coincidence point.

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References

  1. Allgower E.L. and Georg K. (1990). Numerical Continuation Methods: An Introduction. Springer, Berlin

    MATH  Google Scholar 

  2. Arrow K.J. and Hahn F.H. (1971). General Competitive Analysis. Holden-Day, San Francisco

    MATH  Google Scholar 

  3. Doup T. and Talman A.J.J. (1987). A new variable dimension simplicial algorithm to find equilibria on the product space of unit simplices. Math. Program. 37: 319–355

    Article  MATH  MathSciNet  Google Scholar 

  4. Fan K. (1972). A minimax inequality and applications. In: Shisha, O. (eds) Inequalities III, pp 103–113. Academic, New York

    Google Scholar 

  5. Florenzano M. (2003). General Equilibrium Analysis: Existence and Optimality Properties of Equilibra. Kluwer, Boston

    Google Scholar 

  6. Ichiishi T. (1983). Game Theory for Economic Analysis. Academic, New York

    MATH  Google Scholar 

  7. Scarf H. (1967). The approximation of fixed points of a continuous mapping. SIAM J. Appl. Math. 15: 1328–1343

    Article  MATH  MathSciNet  Google Scholar 

  8. Todd M.J. (1976). The Computation of Fixed Points and Applications. Springer, Berlin

    MATH  Google Scholar 

  9. Vohra R. (1991). An existence theorem for a bargaining set. J. Math. Econ. 20: 19–34

    Article  MATH  MathSciNet  Google Scholar 

  10. Wright A.H. (1981). The octahedral algorithm, a new simplicial fixed point algorithm. Math. Program. 21: 47–69

    Article  MATH  Google Scholar 

  11. Yang Z. (1999). Computing Equilibria and Fixed Points. Kluwer, Boston

    MATH  Google Scholar 

  12. Yang Z. (2001). An intersection theorem on an unbounded set and its application to the fair allocation problem. J. Optim. Theory Appl. 110: 429–443

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. CentER, Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands

    A. J. J. Talman

  2. Faculty of Business Administration, Yokohama National University, Yokohama, 240-8501, Japan

    Z. Yang

Authors
  1. A. J. J. Talman
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  2. Z. Yang
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Corresponding author

Correspondence to A. J. J. Talman.

Additional information

This research was carried out while the second author was visiting the CentER for Economic Research, Tilburg University. He would like to thank both CentER and the Netherlands Organization for Scientific Research (NWO) for their financial support.

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Talman, A.J.J., Yang, Z. A constructive proof of Ky Fan’s coincidence theorem. Math. Program. 118, 317–325 (2009). https://doi.org/10.1007/s10107-007-0194-5

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  • DOI: https://doi.org/10.1007/s10107-007-0194-5

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