### Abstract

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.

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

Balkenborg, D., & Vermeulen, A. J. (2014). Universality of Nash components.

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