### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 23 |

Volume | 2008-31 |

Publication status | Published - 2008 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2008-31 |

### Fingerprint

### Keywords

- strategic game
- equilibrium refinement
- blocked action
- fall back equilibrium

### Cite this

*Fall Back Equilibrium*. (CentER Discussion Paper; Vol. 2008-31). Tilburg: Operations research.

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**Fall Back Equilibrium.** / Kleppe, J.; Borm, P.E.M.; Hendrickx, R.L.P.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Fall Back Equilibrium

AU - Kleppe, J.

AU - Borm, P.E.M.

AU - Hendrickx, R.L.P.

N1 - Pagination: 23

PY - 2008

Y1 - 2008

N2 - Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium and show that the set of fall back equilibria is a non-empty and closed subset of the set of Nash equilibria. We discuss the relations with other equilibrium concepts, and among other results it is shown that each robust equilibrium is fall back and for bimatrix games also each proper equilibrium is a fall back equilibrium. Furthermore, we show that for bimatrix games the set of fall back equilibria is the union of finitely many polytopes, and that the notions of fall back equilibrium and strictly fall back equilibrium coincide. Finally, we allow multiple actions to be blocked, resulting in the notion of complete fall back equilibrium. We show that the set of complete fall back equilibria is a non-empty and closed subset of the set of proper equilibria.

AB - Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium and show that the set of fall back equilibria is a non-empty and closed subset of the set of Nash equilibria. We discuss the relations with other equilibrium concepts, and among other results it is shown that each robust equilibrium is fall back and for bimatrix games also each proper equilibrium is a fall back equilibrium. Furthermore, we show that for bimatrix games the set of fall back equilibria is the union of finitely many polytopes, and that the notions of fall back equilibrium and strictly fall back equilibrium coincide. Finally, we allow multiple actions to be blocked, resulting in the notion of complete fall back equilibrium. We show that the set of complete fall back equilibria is a non-empty and closed subset of the set of proper equilibria.

KW - strategic game

KW - equilibrium refinement

KW - blocked action

KW - fall back equilibrium

M3 - Discussion paper

VL - 2008-31

T3 - CentER Discussion Paper

BT - Fall Back Equilibrium

PB - Operations research

CY - Tilburg

ER -