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On Knots and Dynamics in Games

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  • DeMichelis, S.
  • Germano, F.

Abstract

We extend Kohlberg and Mertens' (1986) structure theorem concerning the Nash equilibrium correspondence to show that its graph is not only homomorphic 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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Bibliographic Info

Paper provided by Tel Aviv in its series Papers with number 2-2000.

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Length: 13 pages
Date of creation: 2000
Date of revision:
Handle: RePEc:fth:teavfo:2-2000

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Postal: Israel TEL-AVIV UNIVERSITY, THE FOERDER INSTITUTE FOR ECONOMIC RESEARCH, RAMAT AVIV 69 978 TEL AVIV ISRAEL.
Phone: 972-3-640-9255
Fax: 972-3-640-5815
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Web page: http://econ.tau.ac.il/research/foerder.asp
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Keywords: GAME THEORY ; ECONOMIC EQUILIBRIUM;

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References

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  1. DEMICHELIS, Stefano & GERMANO, Fabrizio, . "On the indices of zeros of Nash fields," CORE Discussion Papers RP -1531, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. 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.
  4. 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).
  5. Samuelson, L. & Zhang, J., 1990. "Evolutionary Stability In Symmetric Games," Working papers 90-24, Wisconsin Madison - Social Systems.
  6. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  7. Joerg Oechssler, 1994. "An Evolutionary Interpretation Of Mixed-Strategy Equilibria," Game Theory and Information 9404001, EconWPA.
  8. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  9. 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.
  10. 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.
  11. Ed Hopkins, . "A Note on Best Response Dynamics," ESE Discussion Papers 3, Edinburgh School of Economics, University of Edinburgh.
  12. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. 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.
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Citations

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Cited by:
  1. 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).
  2. DEMICHELIS, Stefano & RITZBERGER, Klaus, 2000. "From evolutionary to strategic stability," CORE Discussion Papers 2000059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. DE MICHELIS, Stefano, 2000. "On the index and asymptotic stability of dynamics," CORE Discussion Papers 2000018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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