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Minimal farsighted instability

Author

Listed:
  • de Callataÿ, Pierre
  • Mauleon, Ana

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

  • Vannetelbosch, Vincent

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

Abstract

We propose the notion of minimal farsighted instability to determine the states that are more likely to emerge in the long run when agents are farsighted. A state is mini‐ mally farsighted unstable if there is no other state which is more farsightedly stable. To formulate what it means to be more farsightedly stable, we compare states by comparing (in the set inclusion or cardinal sense) their sets of farsighted defeating states. We next compare states in terms of their absorbtiveness by comparing both their sets of farsighted defeating states (i.e. in terms of their stability) and their sets of farsighted defeated states (i.e. in terms of their reachability). A state is maximally farsighted absorbing if there is no other state which is more farsightedly absorbing. We provide general results for characterizing minimally farsighted unstable states and maximally farsighted absorbing states, and we study their relationships with alternative notions of farsightedness. Finally, we use experimental data to show the relevance of the new solution concepts.

Suggested Citation

  • de Callataÿ, Pierre & Mauleon, Ana & Vannetelbosch, Vincent, 2024. "Minimal farsighted instability," LIDAM Reprints CORE 3286, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3286
    DOI: https://doi.org/10.1007/s00182-024-00887-2
    Note: In: International Journal of Game Theory, 2024, vol. 53(2), p. 493-523
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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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