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On knots and dynamics in games

  • DE MICHELIS, Stefano
  • GERMANO, Fabrizio

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.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2000010.

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Date of creation: 01 Feb 2000
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Handle: RePEc:cor:louvco:2000010
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  1. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  2. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
  4. Robert Wilson & Srihari Govindan, 1997. "Uniqueness of the index for Nash equilibria of two-player games," Economic Theory, Springer, vol. 10(3), pages 541-549.
  5. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  7. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
  8. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  9. Kaniovski Yuri M. & Young H. Peyton, 1995. "Learning Dynamics in Games with Stochastic Perturbations," Games and Economic Behavior, Elsevier, vol. 11(2), pages 330-363, November.
  10. DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On the indices of zeros of nash fields," CORE Discussion Papers 2000017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
  12. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer, vol. 23(3), pages 207-36.
  13. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
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