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A fixed point theorem for discontinuous functions

  • HERINGS, P. Jean-Jacques
  • van der LAAN, Gerard
  • TALMAN, Dolf
  • YANG, Zaifu

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.)

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File URL: http://dx.doi.org/10.1016/j.orl.2007.03.008
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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number 2154.

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Handle: RePEc:cor:louvrp:2154
Note: In : Operations Research Letters, 36, 89-93, 2008
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  1. Gérard Debreu (ed.), 1996. "General Equilibrium Theory," Books, Edward Elgar Publishing, volume 0, number 548.
  2. 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.
  3. 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," Discussion Paper 1989-52, Tilburg University, Center for Economic Research.
  4. 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.
  5. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521266550, June.
  6. 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.
  7. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414.
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