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The Theory of Normal Form Games form the Differentiable Viewpoint

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  • Ritzberger, Klaus

Abstract

An alternative definition of regular equilibria is introduced and shown to have the same properties as those definitions already known from the literature. The system of equations used to define regular equilibria induces a globally differentiable structure on the space of mixed strategies. Interpreting this structure as a vector field, called the Nash field, allows for a reproduction of a number of classical results from a differentiable viewpoint. Moreover, approximations of the Nash field can be used to suitably define indices of connected components of equilibria and to identify equilibrium components which are robust against small payoff perturbations.

Suggested Citation

  • Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 207-236.
  • Handle: RePEc:spr:jogath:v:23:y:1994:i:3:p:207-36
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    Citations

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    Cited by:

    1. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
    2. repec:spr:joptap:v:137:y:2008:i:2:d:10.1007_s10957-008-9353-y is not listed on IDEAS
    3. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
    4. Guth, Werner & Kirchsteiger, Georg & Ritzberger, Klaus, 1998. "Imperfectly Observable Commitments inn-Player Games," Games and Economic Behavior, Elsevier, vol. 23(1), pages 54-74, April.
    5. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift and Equilibrium Selection," ELSE working papers 011, ESRC Centre on Economics Learning and Social Evolution.
    6. 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.
    7. Giuseppe De Marco & Jacqueline Morgan, 2007. "Slightly Altruistic Equilibria in Normal Form Games," CSEF Working Papers 185, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    8. Giuseppe De Marco & Jacqueline Morgan, 2009. "On Multicriteria Games with Uncountable Sets of Equilibria," CSEF Working Papers 242, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    9. Elena L. Mercato & Vincenzo Platino, 2017. "On the regularity of smooth production economies with externalities: competitive equilibrium à la Nash," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 287-307, January.
    10. Yannick Viossat, 2005. "Openness of the set of games with a unique correlated equilibrium," Working Papers hal-00243016, HAL.
    11. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    12. 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).
    13. Stefano Demichelis & Klaus Ritzberger & Jeroen M. Swinkels, 2004. "The simple geometry of perfect information games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 315-338, June.
    14. 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).
    15. 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.
    16. Demichelis, Stefano & Germano, Fabrizio, 2002. "On (un)knots and dynamics in games," Games and Economic Behavior, Elsevier, vol. 41(1), pages 46-60, October.
    17. Elena L. Del Mercato & Vincenzo Platino, 2016. "On the regularity of smooth production economies with externalities: Competitive equilibrium à la Nash," Post-Print halshs-01162039, HAL.
    18. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    19. Dieter Balkenborg & Dries Vermeulen, 2016. "Where Strategic and Evolutionary Stability Depart—A Study of Minimal Diversity Games," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 278-292, February.
    20. 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.
    21. Gaël Giraud, 2000. "Notes sur les jeux stratégiques de marchés," Cahiers d'Économie Politique, Programme National Persée, vol. 37(1), pages 257-272.

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