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Local contraction-stability and uniqueness


  • Andreas M. Hefti


This paper investigates the relationship between uniqueness of Nash equilibria and local stability with respect to the best-response dynamics in the cases of sum-aggregative and symmetric games. If strategies are equilibrium complements, local stability and uniqueness are the same formal properties of the game. With equilibrium substitutes, local stability is stronger than uniqueness. If players adjust sequentially rather than simultaneously, this tends towards making a symmetric equilibria of symmetric games more stable. Finally, the relationship between the stability of the Nash best-response dynamics is compared to the stability of the response-dynamics induced by aggregate-taking behavior.

Suggested Citation

  • Andreas M. Hefti, 2013. "Local contraction-stability and uniqueness," ECON - Working Papers 112, Department of Economics - University of Zurich.
  • Handle: RePEc:zur:econwp:112

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    References listed on IDEAS

    1. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    2. Diewert, W. E. & Avriel, M. & Zang, I., 1981. "Nine kinds of quasiconcavity and concavity," Journal of Economic Theory, Elsevier, vol. 25(3), pages 397-420, December.
    3. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    4. M. McManus & Richard E. Quandt, 1961. "Comments on the Stability of the Cournot Oligipoly Model," Review of Economic Studies, Oxford University Press, vol. 28(2), pages 136-139.
    5. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 497-516, October.
    6. Andreas Hefti, 2011. "On uniqueness and stability of symmetric equilibria in differentiable symmetric games," ECON - Working Papers 018, Department of Economics - University of Zurich.
    7. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
    8. Okuguchi, Koji & Yamazaki, Takeshi, 2008. "Global stability of unique Nash equilibrium in Cournot oligopoly and rent-seeking game," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1204-1211, April.
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    More about this item


    Contraction mapping; stability; uniqueness; aggregate-taking behavior; dominance solvability; symmetric games;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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