### Abstract

We introduce the concept of a horizon-K farsighted set to study the influence of the degree of farsightedness on network stability. The concept generalizes existing concepts where all players are either fully myopic or fully farsighted. A set of networks GK is a horizon-K farsighted set if three conditions are satisfied. First, external deviations should be horizon-K deterred. Second, from any network outside of GK there is a sequence of farsighted improving paths of length smaller than or equal to K leading to some network in GK. Third, there is no proper subset of GK satisfying the first two conditions. We show that a horizon-K farsighted set always exists and that the horizon-1 farsighted set G1 is always unique. For generic allocation rules, the set G1 always contains a horizon-K farsighted set for any K. We provide easy to verify conditions for a set of networks to be a horizon-K farsighted set, and we consider the efficiency of networks in horizon-K farsighted sets. We discuss the effects of players with different horizons in an example of criminal networks.

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

Pages (from-to) | 177-201 |

Number of pages | 25 |

Journal | Economic Theory |

Volume | 68 |

Issue number | 1 |

Early online date | 17 Apr 2018 |

DOIs | |

Publication status | Published - Jul 2019 |

### Keywords

- Limited farsightedness
- Stability
- Efficiency
- Networks
- STABLE SETS

## Cite this

*Economic Theory*,

*68*(1), 177-201. https://doi.org/10.1007/s00199-018-1119-7