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
Allgower E.L. and Georg K. (1990). Numerical Continuation Methods: An Introduction. Springer, Berlin
Arrow K.J. and Hahn F.H. (1971). General Competitive Analysis. Holden-Day, San Francisco
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
Fan K. (1972). A minimax inequality and applications. In: Shisha, O. (eds) Inequalities III, pp 103–113. Academic, New York
Florenzano M. (2003). General Equilibrium Analysis: Existence and Optimality Properties of Equilibra. Kluwer, Boston
Ichiishi T. (1983). Game Theory for Economic Analysis. Academic, New York
Scarf H. (1967). The approximation of fixed points of a continuous mapping. SIAM J. Appl. Math. 15: 1328–1343
Todd M.J. (1976). The Computation of Fixed Points and Applications. Springer, Berlin
Vohra R. (1991). An existence theorem for a bargaining set. J. Math. Econ. 20: 19–34
Wright A.H. (1981). The octahedral algorithm, a new simplicial fixed point algorithm. Math. Program. 21: 47–69
Yang Z. (1999). Computing Equilibria and Fixed Points. Kluwer, Boston
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
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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