### 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 language | English |
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Pages (from-to) | 278-292 |

Number of pages | 15 |

Journal | Mathematics of Operations Research |

Volume | 41 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 2016 |

### Keywords

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