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Myopic-farsighted absorbing networks

Author

Listed:
  • de Callataÿ, Pierre

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Mauleon, Ana

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Vannetelbosch, Vincent

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

We propose the notion of myopic-farsighted absorbing set to determine the networks that emerge in the long run when some players are myopic while others are farsighted. A set of networks is a myopic-farsighted absorbing set if (No External Deviation) there is no myopic-farsighted improving path from networks within the set to some networks outside the set, (External Stability) there is a myopic-farsighted improving path from any network outside the set to some network within the set, and (Minimality) there is no proper subset satisfying No External Deviation and External Stability. Contrary to the notion of myopic-farsighted stable set, we show that a myopic-farsighted absorbing set always exists. We partially characterize the myopic-farsighted absorbing sets and we provide sufficient conditions for the equivalence between a myopic-farsighted absorbing set and a myopic-farsighted stable set. We also introduce and fully characterize the notion of proper myopic-farsighted absorbing set that refines the concept of myopic-farsighted absorbing set by selecting the more absorbing networks. Finally, we consider a threshold game that illustrates the role of the relative number of farsighted and myopic players for reaching efficiency.

Suggested Citation

  • de Callataÿ, Pierre & Mauleon, Ana & Vannetelbosch, Vincent, 2022. "Myopic-farsighted absorbing networks," LIDAM Reprints CORE 3215, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3215
    DOI: https://doi.org/10.1007/s11238-022-09895-8
    Note: In: Theory and Decision, 2022
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    Cited by:

    1. is not listed on IDEAS
    2. Michel Grabisch & Elena Parilina & Agnieszka Rusinowska & Georges Zaccour, 2025. "Dynamic Network Formation with Farsighted Players and Limited Capacities," Documents de travail du Centre d'Economie de la Sorbonne 25019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. 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.

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    JEL classification:

    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D20 - Microeconomics - - Production and Organizations - - - General

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