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

Dieter Balkenborg, Dries Vermeulen

Research output: Contribution to journalArticleAcademicpeer-review

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.
Original languageEnglish
Pages (from-to)278-292
Number of pages15
JournalMathematics of Operations Research
Volume41
Issue number1
DOIs
Publication statusPublished - Feb 2016

Keywords

  • strategic form games
  • strategic stability
  • evolutionary stability
  • EQUILIBRIUM POINTS
  • STABLE EQUILIBRIA
  • DEFINITION
  • REFORMULATION
  • SELECTION

Cite this

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title = "Where Strategic and Evolutionary Stability Depart-A Study of Minimal Diversity Games",
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.",
keywords = "strategic form games, strategic stability, evolutionary stability, EQUILIBRIUM POINTS, STABLE EQUILIBRIA, DEFINITION, REFORMULATION, SELECTION",
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Where Strategic and Evolutionary Stability Depart-A Study of Minimal Diversity Games. / Balkenborg, Dieter; Vermeulen, Dries.

In: Mathematics of Operations Research, Vol. 41, No. 1, 02.2016, p. 278-292.

Research output: Contribution to journalArticleAcademicpeer-review

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KW - strategic form games

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