Advanced Search
MyIDEAS: Login to save this article or follow this journal

From evolutionary to strategic stability

Contents:

Author Info

  • Demichelis, Stefano
  • Ritzberger, Klaus

Abstract

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.

(This abstract was borrowed from another version of this item.)

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.sciencedirect.com/science/article/B6WJ3-48N2RT8-B/2/67f27d3c0a3f309488218b4fdf28efec
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 113 (2003)
Issue (Month): 1 (November)
Pages: 51-75

as in new window
Handle: RePEc:eee:jetheo:v:113:y:2003:i:1:p:51-75

Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords:

Other versions of this item:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  2. Arthur J Robson & Fernando Vega-Redondo, 1999. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Levine's Working Paper Archive 2112, David K. Levine.
  3. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  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. 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.
  6. Dieter Balkenborg & Karl H. Schlag, 2001. "On the Evolutionary Selection of Nash Equilibrium Components," Discussion Papers 0106, Exeter University, Department of Economics.
  7. J. Maynard Smith, 2010. "The Theory of Games and Evolution of Animal Conflicts," Levine's Working Paper Archive 448, David K. Levine.
  8. 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.
  9. Cressman, R. & Schlag, K. H., 1998. "The Dynamic (In)Stability of Backwards Induction," Journal of Economic Theory, Elsevier, vol. 83(2), pages 260-285, December.
  10. 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.
  11. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
  12. Damme, E.E.C. van, 1989. "Stable equilibria and forward induction," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154422, Tilburg University.
  13. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  14. 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.
  15. Cho, In-Koo & Kreps, David M, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 179-221, May.
  16. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
  17. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  18. Damme, E.E.C. van, 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154427, Tilburg University.
  19. repec:fth:louvco:2000/10 is not listed on IDEAS
  20. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
  21. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  22. 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.
  23. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
  24. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  25. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  26. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-90, November.
  27. MERTENS, Jean-François, . "Localization of the degree on lower-dimensional sets," CORE Discussion Papers RP -1740, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  28. 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.
  29. 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.
  30. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
  31. repec:fth:louvco:2000/17 is not listed on IDEAS
  32. 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.
  33. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  34. Fudenberg, Drew & Harris, Christopher, 1992. "Evolutionary Dynamics with Aggregate Shocks," IDEI Working Papers 13, Institut d'Économie Industrielle (IDEI), Toulouse.
  35. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  36. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
  37. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
  38. 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).
  39. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  40. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  41. 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.
  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.
  43. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
  44. D. Foster & P. Young, 2010. "Stochastic Evolutionary Game Dynamics," Levine's Working Paper Archive 493, David K. Levine.
  45. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Geir B. , Asheim & Voorneveld, Max & W. Weibull, Jörgen, 2009. "Epistemically Stable Strategy Sets," Memorandum 01/2010, Oslo University, Department of Economics.
  2. Stefano Demichelis & Klaus Ritzberger & Jeroen M. Swinkels, 2004. "The simple geometry of perfect information games," International Journal of Game Theory, Springer, vol. 32(3), pages 315-338, 06.
  3. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.
  4. Kuzmics, Christoph, 2004. "Stochastic evolutionary stability in extensive form games of perfect information," Games and Economic Behavior, Elsevier, vol. 48(2), pages 321-336, August.
  5. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
  6. Dieter Balkenborg & Stefano Demichelis & Dries Vermeulen, 2010. "Where strategic and evolutionary stability depart - a study of minimal diversity games," Discussion Papers 1001, Exeter University, Department of Economics.
  7. Demichelis, Stefano & Germano, Fabrizio, 2002. "On (un)knots and dynamics in games," Games and Economic Behavior, Elsevier, vol. 41(1), pages 46-60, October.
  8. Stefano Demichelis, 2012. "Evolution towards asymptotic efficiency, preliminary version," Quaderni di Dipartimento 173, University of Pavia, Department of Economics and Quantitative Methods.
  9. Jens Josephson, 2008. "Stochastic better-reply dynamics in finite games," Economic Theory, Springer, vol. 35(2), pages 381-389, May.
  10. Dieter Balkenborg & Dries Vermeulen, 2012. "Universality of Nash Components," Discussion Papers 1205, Exeter University, Department of Economics.
  11. Demichelis, Stefano, 2012. "Evolution towards efficient coordination in repeated games, preliminary version," MPRA Paper 39311, University Library of Munich, Germany.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:113:y:2003:i:1:p:51-75. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.