### 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

}

*Economic Theory*, vol. 68, no. 1, pp. 177-201. https://doi.org/10.1007/s00199-018-1119-7

**Stability of networks under horizon-K farsightedness.** / Herings, P. Jean-Jacques; Mauleon, Ana; Vannetelbosch, Vincent.

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

TY - JOUR

T1 - Stability of networks under horizon-K farsightedness

AU - Herings, P. Jean-Jacques

AU - Mauleon, Ana

AU - Vannetelbosch, Vincent

N1 - data source: no data used

PY - 2019/7

Y1 - 2019/7

N2 - 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.

AB - 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.

KW - Limited farsightedness

KW - Stability

KW - Efficiency

KW - Networks

KW - STABLE SETS

U2 - 10.1007/s00199-018-1119-7

DO - 10.1007/s00199-018-1119-7

M3 - Article

VL - 68

SP - 177

EP - 201

JO - Economic Theory

JF - Economic Theory

SN - 0938-2259

IS - 1

ER -