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On knots and dynamics in games

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  • DE MICHELIS, Stefano
  • GERMANO, Fabrizio
Abstract
We extend Kohlberg and Mertens' (1986) structure theorem concerning the Nash equilibrium correspondence to show that its graph is not only homeomorphic to the underlying space of games but that it is also unknotted. This is then shown to have some basic consequences for dynamics whose rest points are Nash equilibria.

Suggested Citation

  • DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On knots and dynamics in games," LIDAM Discussion Papers CORE 2000010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2000010
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    References listed on IDEAS

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    1. DeMichelis, Stefano & Germano, Fabrizio, 2000. "On the Indices of Zeros of Nash Fields," Journal of Economic Theory, Elsevier, vol. 94(2), pages 192-217, October.
    2. David Besanko & Ulrich Doraszelski, 2005. "Learning-by-Doing, Organizational Forgetting, and Industry Dynanmics," Computing in Economics and Finance 2005 236, Society for Computational Economics.
    3. Predtetchinski, Arkadi, 2009. "A general structure theorem for the Nash equilibrium correspondence," Games and Economic Behavior, Elsevier, vol. 66(2), pages 950-958, July.
    4. Bich, Philippe & Fixary, Julien, 2022. "Network formation and pairwise stability: A new oddness theorem," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    5. Stefano Demichelis & Amrita Dhillon, 2010. "Learning in Elections and Voter Turnout," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(5), pages 871-896, October.
    6. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov & Mark Satterthwaite, 2007. "Learning-by-Doing, Organizational Forgetting, and Industry Dynamics," Levine's Bibliography 321307000000000903, UCLA Department of Economics.
    7. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov & Mark Satterthwaite, 2008. "Learning-by-Doing, Organizational Forgetting, and Industry Dynamics," GSIA Working Papers 2009-E22, Carnegie Mellon University, Tepper School of Business.
    8. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    9. DE MICHELIS, Stefano, 2000. "On the index and asymptotic stability of dynamics," LIDAM Discussion Papers CORE 2000018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Sun, Ching-jen, 2020. "A sandwich theorem for generic n × n two person games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 86-95.
    11. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.

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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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