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Strongly rational sets for normal-form games

Author

Listed:
  • GRANDJEAN, Gilles

    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • MAULEON, Ana

    (FNRS and Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • VANNETELBOSCH, Vincent

    (FNRS and Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

Abstract

Curb sets [Basu and Weibull, Econ. Letters 36 (1991), 141-146] are product sets of pure strategies containing all individual best-responses against beliefs restricted to the recommendations to the remaining players. The concept of minimal curb sets is a set-theoretic coarsening of the notion of strict Nash equilibrium. We introduce the concept of minimal strong curb sets which is a set-theoretic coarsening of the notion of strong Nash equilibrium. Strong curb sets are product sets of pure strategies such that each player's set of recommended strategies must contain all coalitional best-responses of each coalition to whatever belief each coalition member may have that is consistent with the recommendations to the other players. Minimal strong curb sets are shown to exist and are compared with other well known solution concepts. We also provide a dynamic learning process leading the players to playing strategies from a minimal strong curb set.

Suggested Citation

  • GRANDJEAN, Gilles & MAULEON, Ana & VANNETELBOSCH, Vincent, 2009. "Strongly rational sets for normal-form games," LIDAM Discussion Papers CORE 2009066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2009066
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    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
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    More about this item

    Keywords

    set-valued solution concept; coalitional best-response; strong curb set; learning;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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