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Stability of networks under level-k farsightedness

Author

Listed:
  • Herings, P.J.J.

    (Microeconomics & Public Economics)

  • Mauleon, A.

    (Externe publicaties SBE)

  • Vannetelbosch, V.

    (Externe publicaties SBE)

Abstract

We provide a tractable concept that can be used to study the influence of the degree of farsightedness on network stability. A set of networks GK is a level-K farsightedly stable set if three conditions are satisfied. First, external deviations should be 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 level-K farsightedly stable set always exists and we provide a sufficient condition for the uniqueness of a level-K farsightedly stable set. There is a unique level-1 farsightedly stable set G1 consisting of all networks that belong to closed cycles. Level-K farsighted stability leads to a refinement of G1 for generic allocation rules. We then provide easy to verify conditions for a set to be level-K farsightedly stable and we consider the relationship between level-K farsighted stability and efficiency of networks. We show the tractability of the concept by applying it to a model of criminal networks.

Suggested Citation

  • Herings, P.J.J. & Mauleon, A. & Vannetelbosch, V., 2014. "Stability of networks under level-k farsightedness," Research Memorandum 030, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2014030
    DOI: 10.26481/umagsb.2014030
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    Cited by:

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    3. Mariya Teteryatnikova, 2015. "Cautious Farsighted Stability in Network Formation Games with Streams of Payoffs," Vienna Economics Papers 1509, University of Vienna, Department of Economics.
    4. Mariya Teteryatnikova, 2015. "Cautious Farsighted Stability in Network Formation Games with Streams of Payoffs," Vienna Economics Papers vie1509, University of Vienna, Department of Economics.
    5. Stefan Berens & Lasha Chochua & Gerald Willmann, 2021. "The Farsighted Stability of Global Tade Policy Arrangements," CESifo Working Paper Series 9213, CESifo.
    6. Mariya Teteryatnikova, 2021. "Cautious farsighted stability in network formation games with streams of payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 829-865, December.
    7. Berens, Stefan & Chochua, Lasha & Willmann, Gerald, 2021. "The farsighted stability of global trade policy arrangements," Kiel Working Papers 2193, Kiel Institute for the World Economy (IfW Kiel).

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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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