Stability of networks under horizon-K farsightedness

P. Jean-Jacques Herings, Ana Mauleon, Vincent Vannetelbosch

Research output: Contribution to journalArticleAcademicpeer-review

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 languageEnglish
Pages (from-to)177-201
Number of pages25
JournalEconomic Theory
Volume68
Issue number1
Early online date17 Apr 2018
DOIs
Publication statusPublished - Jul 2019

Keywords

  • Limited farsightedness
  • Stability
  • Efficiency
  • Networks
  • STABLE SETS

Cite this

Herings, P. Jean-Jacques ; Mauleon, Ana ; Vannetelbosch, Vincent. / Stability of networks under horizon-K farsightedness. In: Economic Theory. 2019 ; Vol. 68, No. 1. pp. 177-201.
@article{d585e1ceb24a4b64898635b5b952ae3a,
title = "Stability of networks under horizon-K farsightedness",
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.",
keywords = "Limited farsightedness, Stability, Efficiency, Networks, STABLE SETS",
author = "Herings, {P. Jean-Jacques} and Ana Mauleon and Vincent Vannetelbosch",
note = "data source: no data used",
year = "2019",
month = "7",
doi = "10.1007/s00199-018-1119-7",
language = "English",
volume = "68",
pages = "177--201",
journal = "Economic Theory",
issn = "0938-2259",
publisher = "Springer Verlag",
number = "1",

}

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

In: Economic Theory, Vol. 68, No. 1, 07.2019, p. 177-201.

Research output: Contribution to journalArticleAcademicpeer-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 -