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Two simple proofs of the feasibility of the linear tracing procedure


  • P. Jean-Jacques Herings

    () (Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, NL-5000 LE Tilburg, THE NETHERLANDS)


Theories of equilibrium selection in non-cooperative games, as well as the notion of risk dominance, depend heavily on the so-called linear tracing procedure. This is the first paper to give direct, simple proofs of the feasibility of the linear tracing procedure. The first proof utilizes a result that is related to Kakutani's fixed point theorem and that is an extension of Browder's fixed point theorem. The second proof shows that it is even possible to avoid the use of correspondences.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:15:y:2000:i:2:p:485-490 Note: Received: June 8, 1998; revised version: November 8, 1998

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    References listed on IDEAS

    1. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
    2. Jones, Ronald W, 1970. "The Transfer Problem Revisited," Economica, London School of Economics and Political Science, vol. 37(146), pages 178-184, May.
    3. Timothy J. Kehoe, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, Oxford University Press, vol. 100(1), pages 119-147.
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    Cited by:

    1. Herings,P. Jean-Jacques, 2000. "Universally Stable Adjustment Processes - A Unifying Approach -," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. 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.
    3. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    4. Jean-Jacques Herings, P., 2002. "Universally converging adjustment processes--a unifying approach," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 341-370, November.
    5. Yin Chen & Chuangyin Dang, 2016. "A reformulation-based smooth path-following method for computing Nash equilibria," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 231-246, October.

    More about this item


    Non-cooperative game theory; Tracing procedure; Equilibrium selection; Browder's fixed point theorem.;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games


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