### Abstract

Original language | English |
---|---|

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

### Cite this

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*Mathematics of Operations Research*, vol. 41, no. 1, pp. 278-292. https://doi.org/10.1287/moor.2015.0727

**Where Strategic and Evolutionary Stability Depart-A Study of Minimal Diversity Games.** / Balkenborg, Dieter; Vermeulen, Dries.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Where Strategic and Evolutionary Stability Depart-A Study of Minimal Diversity Games

AU - Balkenborg, Dieter

AU - Vermeulen, Dries

N1 - no data used

PY - 2016/2

Y1 - 2016/2

N2 - 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.

AB - 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.

KW - strategic form games

KW - strategic stability

KW - evolutionary stability

KW - EQUILIBRIUM POINTS

KW - STABLE EQUILIBRIA

KW - DEFINITION

KW - REFORMULATION

KW - SELECTION

U2 - 10.1287/moor.2015.0727

DO - 10.1287/moor.2015.0727

M3 - Article

VL - 41

SP - 278

EP - 292

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

SN - 0364-765X

IS - 1

ER -