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Two simple proofs of the feasibility of the linear tracing procedure

Author

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  • P. Jean-Jacques Herings

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

Abstract

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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    Cited by:

    1. Yiyin Cao & Yin Chen & Chuangyin Dang, 2024. "A Differentiable Path-Following Method with a Compact Formulation to Compute Proper Equilibria," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 377-396, March.
    2. Yiyin Cao & Yin Chen & Chuangyin Dang, 2024. "A Variant of the Logistic Quantal Response Equilibrium to Select a Perfect Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1026-1062, June.
    3. Peixuan Li & Chuangyin Dang, 2020. "An Arbitrary Starting Tracing Procedure for Computing Subgame Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 667-687, August.
    4. Boone, C.A.J.J. & Roijakkers, A.H.W.M. & van Olffen, W., 2002. "Locus of control and study program choice: evidence of personality sorting in educational choice," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. Peixuan Li & Chuangyin Dang & P. Jean-Jacques Herings, 2024. "Computing perfect stationary equilibria in stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 347-387, September.
    6. Friedel Bolle, 2022. "Voting with abstention," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(1), pages 30-57, February.
    7. 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.
    8. Yiyin Cao & Chuangyin Dang, 2025. "A Characterization of Nash Equilibrium in Behavioral Strategies through Local Sequential Rationality," Papers 2504.00529, arXiv.org, revised Apr 2025.
    9. Yin Chen & Chuangyin Dang, 2019. "A Reformulation-Based Simplicial Homotopy Method for Approximating Perfect Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 877-891, October.
    10. 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.
    11. Herings, P. J. J. & Polemarchakis, H., 2002. "Equilibrium and arbitrage in incomplete asset markets with fixed prices," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 133-155, April.
    12. Mark Voorneveld, 2006. "Probabilistic Choice in Games: Properties of Rosenthal’s t-Solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 105-121, April.
    13. Jean-Jacques Herings, P., 2002. "Universally converging adjustment processes--a unifying approach," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 341-370, November.
    14. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    15. 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).
    16. Yiyin Cao & Chuangyin Dang & Yabin Sun, 2022. "Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 533-563, February.
    17. Cao, Yiyin & Dang, Chuangyin, 2022. "A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 134(C), pages 127-150.

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    JEL classification:

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

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