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From evolutionary to strategic stability

  • DEMICHELIS, Stefano

A component of Nash equilibria is (dynamically) potentially stable if there exists an evolutionary selection dynamics from a broad class for which the component is asymptotically stable. A necessary condition for potential stability is that the component's index agrees with its Euler characteristic. Second, if the latter is nonzero, the component contains a strategically stable set. If the Euler characteristic would be zero, the dynamics (which justifies potential stability) could be slightly perturbed so as to remove all zeros close to the component. Hence, any robustly potentially stable component contains equilibria which satisfy the strongest rationalistic refinement criteria.

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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 2000059.

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Date of creation: 01 Dec 2000
Date of revision:
Handle: RePEc:cor:louvco:2000059
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  1. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
  2. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, June.
  3. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
  4. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
  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. Mertens, J.-F., 1986. "Localization of the degree on lower-dimensional sets," CORE Discussion Papers 1986005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
  8. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  9. 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.
  10. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-94, July.
  11. Dieter Balkenborg & Karl H. Schlag, 2001. "On the Evolutionary Selection of Nash Equilibrium Components," Discussion Papers 0106, Exeter University, Department of Economics.
  12. D. Foster & P. Young, 2010. "Stochastic Evolutionary Game Dynamics," Levine's Working Paper Archive 493, David K. Levine.
  13. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  14. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
  15. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  16. R. Cressman & K.H. Schlag, . "The Dynamic (In)Stability of Backwards Induction," ELSE working papers 027, ESRC Centre on Economics Learning and Social Evolution.
  17. Fudenberg, Drew & Harris, Christopher, 1992. "Evolutionary Dynamics with Aggregate Shocks," IDEI Working Papers 13, Institut d'Économie Industrielle (IDEI), Toulouse.
  18. In-Koo Cho & David M. Kreps, 1997. "Signaling Games and Stable Equilibria," Levine's Working Paper Archive 896, David K. Levine.
  19. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  20. DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On knots and dynamics in games," CORE Discussion Papers 2000010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  21. George J. Mailath, . ""Do People Play Nash Equilibrium? Lessons From Evolutionary Game Theory''," CARESS Working Papres 98-01, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  22. Jeroen M. Swinkels, 1991. "Adjustment Dynamics and Rational Play in Games," Discussion Papers 1001, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  23. Boylan, Richard T., 1990. "Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals," Working Papers 748, California Institute of Technology, Division of the Humanities and Social Sciences.
  24. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
  25. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  26. Hauk, Esther & Hurkens, Sjaak, 2002. "On Forward Induction and Evolutionary and Strategic Stability," Journal of Economic Theory, Elsevier, vol. 106(1), pages 66-90, September.
  27. Sergiu Hart, 1999. "Evolutionary Dynamics and Backward Induction," Game Theory and Information 9905002, EconWPA, revised 23 Mar 2000.
  28. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
  29. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  30. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
  31. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
  32. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
  33. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-90, November.
  34. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
  35. Boylan Richard T., 1995. "Continuous Approximation of Dynamical Systems with Randomly Matched Individuals," Journal of Economic Theory, Elsevier, vol. 66(2), pages 615-625, August.
  36. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
  37. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  38. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
  39. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  40. George J. Mailath, 1998. "Corrigenda [Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory]," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 1941-1941, December.
  41. J. Maynard Smith, 2010. "The Theory of Games and Evolution of Animal Conflicts," Levine's Working Paper Archive 448, David K. Levine.
  42. 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.
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