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Local contraction-stability and uniqueness

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  • Andreas M. Hefti

Abstract

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
    as

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    File URL: https://www.zora.uzh.ch/id/eprint/74251/1/econwp112.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Contraction mapping; stability; uniqueness; aggregate-taking behavior; dominance solvability; symmetric games;
    All these keywords.

    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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