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Stability of networks under horizon-K farsightedness
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Stability of networks under horizon-K farsightedness

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

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 $$G_{K}$$ G K 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 $$G_{K}$$ G K there is a sequence of farsighted improving paths of length smaller than or equal to K leading to some network in $$G_{K}$$ G K . Third, there is no proper subset of $$G_{K}$$ G K satisfying the first two conditions. We show that a horizon-K farsighted set always exists and that the horizon-1 farsighted set $$G_{1}$$ G 1 is always unique. For generic allocation rules, the set $$G_{1}$$ G 1 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.
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Suggested Citation

  • P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2019. "Stability of networks under horizon-K farsightedness," LIDAM Reprints CORE 3026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3026
    Note: In : Economic Theory, 68, 177-201, 2019
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    Cited by:

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    2. Mert Kimya, 2023. "Coalition Formation Under Dominance Invariance," Dynamic Games and Applications, Springer, vol. 13(2), pages 480-496, June.
    3. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2021. "Horizon- K Farsightedness in Criminal Networks," Games, MDPI, vol. 12(3), pages 1-13, July.
    4. David Pérez-Castrillo & Marilda Sotomayor, 2023. "Constrained-optimal tradewise-stable outcomes in the one-sided assignment game: a solution concept weaker than the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 963-994, October.
    5. Zhang, Qian & Cheng, Baodong & Diao, Gang & Tao, Chenlu & Wang, Can, 2023. "Does China's natural forest logging ban affect the stability of the timber import trade network?," Forest Policy and Economics, Elsevier, vol. 152(C).
    6. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 2022. "Coalition-proof stable networks," Review of Economic Design, Springer;Society for Economic Design, vol. 26(2), pages 185-209, June.
    7. Ata Atay & Ana Mauleon & Vincent Vannetelbosch, 2022. "Limited Farsightedness in Priority-Based Matching," Papers 2212.07427, arXiv.org.
    8. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2023. "Social Rationalizability with Mediation," Dynamic Games and Applications, Springer, vol. 13(2), pages 440-461, June.
    9. Mauleon, Ana & Sempere-Monerris, Jose J. & Vannetelbosch, Vincent, 2023. "R&D network formation with myopic and farsighted firms," Journal of Economic Behavior & Organization, Elsevier, vol. 208(C), pages 203-229.
    10. Pierre de Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2023. "Myopic-farsighted absorbing networks," Theory and Decision, Springer, vol. 94(3), pages 405-422, April.
    11. Hirai, Toshiyuki & Watanabe, Naoki & Muto, Shigeo, 2019. "Farsighted stability in patent licensing: An abstract game approach," Games and Economic Behavior, Elsevier, vol. 118(C), pages 141-160.
    12. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    13. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 2021. "Network formation with myopic and farsighted players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1283-1317, June.
    14. Francis Bloch & Ana Mauleon & Vincent Vannetelbosch, 2023. "Preface to the Special issue on “Group Formation and Farsightedness”," Dynamic Games and Applications, Springer, vol. 13(2), pages 435-439, June.
    15. Ana Mauleon & Jose J. Sempere-Monerris & Vincent Vannetelbosch, 2023. "Limited Farsightedness in R &D Network Formation," Dynamic Games and Applications, Springer, vol. 13(2), pages 549-565, June.
    16. Ana Mauleon & Simon Schopohl & Akylai Taalaibekova & Vincent Vannetelbosch, 2022. "Coordination on networks with farsighted and myopic agents," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 509-536, November.
    17. Pierre Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2024. "Minimal farsighted instability," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 493-523, June.
    18. de Callatay, Pierre & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "Minimally Farsighted Unstable Networks," LIDAM Discussion Papers CORE 2021012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 2021-06, University of Sydney, School of Economics.
    20. Luo, Chenghong & Mauleon, Ana & Vannetelbosch, Vincent, 2024. "Destabilizing segregation in friendship networks with farsighted agents," Journal of Economic Behavior & Organization, Elsevier, vol. 221(C), pages 1-16.
    21. Cai, Xinyue & Kimya, Mert, 2023. "Stability of alliance networks," Games and Economic Behavior, Elsevier, vol. 140(C), pages 401-409.
    22. Pierre de Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2024. "Local farsightedness in network formation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 20(2), pages 199-226, June.
    23. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 202106, University of Sydney, School of Economics.
    24. Luo, Chenghong & Mauleon, Ana & Vannetelbosch, Vincent, 2022. "Friendship networks with farsighted agents," LIDAM Discussion Papers CORE 2022021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
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