### Abstract

We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k.

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

Pages (from-to) | 67-76 |

Journal | Games and Economic Behavior |

Volume | 86 |

DOIs | |

Publication status | Published - 1 Jan 2014 |

### Cite this

*Games and Economic Behavior*,

*86*, 67-76. https://doi.org/10.1016/j.geb.2014.03.010

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*Games and Economic Behavior*, vol. 86, pp. 67-76. https://doi.org/10.1016/j.geb.2014.03.010

**Universality of Nash components.** / Balkenborg, D.; Vermeulen, A.J.

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

TY - JOUR

T1 - Universality of Nash components

AU - Balkenborg, D.

AU - Vermeulen, A.J.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game-a game where all players have two pure strategies and a common utility function with values either zero or one-whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k.

AB - We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game-a game where all players have two pure strategies and a common utility function with values either zero or one-whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k.

U2 - 10.1016/j.geb.2014.03.010

DO - 10.1016/j.geb.2014.03.010

M3 - Article

VL - 86

SP - 67

EP - 76

JO - Games and Economic Behavior

JF - Games and Economic Behavior

SN - 0899-8256

ER -