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Where strategic and evolutionary stability depart - a study of minimal diversity games

Author

Listed:
  • Dieter Balkenborg

    (Department of Economics, University of Exeter)

  • Stefano Demichelis

    (Department of Mathematics, University of Pavia)

  • Dries Vermeulen

    (Department of Quantitative Economics, University Maastricht)

Abstract

A minimal diversity game is an n player strategic form game in which each player has m pure strategies at his disposal. The payoff to each player is always 1, unless all players select the same pure strategy, in which case all players receive zero payoff. Such a game has a unique isolated completely mixed Nash equilibrium in which each player plays each strategy with equal probability, and a connected component of Nash equilibria consisting of those strategy profiles in which each player receives payoff 1. The Pareto superior component is shown to be asymptotically stable under a wide class of evolutionary dynamics, while the isolated equilibrium is not. On the other hand, the isolated equilibrium is strategically stable, while the strategic stability of the Pareto efficient component depends on the dimension of the component, and hence on the number of players, and the number of pure strategies.

Suggested Citation

  • Dieter Balkenborg & Stefano Demichelis & Dries Vermeulen, 2010. "Where strategic and evolutionary stability depart - a study of minimal diversity games," Discussion Papers 1001, University of Exeter, Department of Economics.
    • Handle: RePEc:exe:wpaper:1001
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    File URL: https://exetereconomics.github.io/RePEc/dpapers/DP1001.pdf
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    References listed on IDEAS

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    Cited by:

    1. Man, Priscilla T.Y., 2012. "Efficiency and stochastic stability in normal form games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 272-284.

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    More about this item

    Keywords

    Strategic form games; strategic stability; evolutionary stability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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