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Where Strategic and Evolutionary Stability Depart—A Study of Minimal Diversity Games

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  • Dieter Balkenborg

    (Department of Economics, University of Exeter, Exeter EX4 4PU, United Kingdom)

  • Dries Vermeulen

    (Department of Quantitative Economics, University Maastricht, 6200 MD Maastricht, Netherlands)

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. In contrast, 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.

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  • 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.
    • Handle: RePEc:inm:ormoor:v:41:y:2016:i:1:p:278-292
    DOI: 10.1287/moor.2015.0727
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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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