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Finding all minimal curb sets


  • Max Klimm

    (MPII - Max-Planck-Institut für Informatik - Max-Planck-Institut)

  • Jörgen Weibull

    (SSE - Department of Economics - Stockholm School of Economics, Department of Economics, Ecole Polytechnique - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique)


Sets closed under rational behavior were introduced by Basu and Weibull (1991) as subsets of the strategy space that contain all best replies to all strategy profiles in the set. We here consider a more restrictive notion of closure under rational behavior: a subset of the strategy space is strongly closed under rational behavior, or sCURB, if it contains all best replies to all probabilistic beliefs over the set. We present an algorithm that computes all minimal sCURB sets in any given finite game. Runtime measurements on two-player games (where the concepts of CURB and sCURB coincide) show that the algorithm is considerably faster than the earlier developed algorithm, that of Benisch et al. (2006).

Suggested Citation

  • Max Klimm & Jörgen Weibull, 2009. "Finding all minimal curb sets," Working Papers hal-00442118, HAL.
  • Handle: RePEc:hal:wpaper:hal-00442118
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    References listed on IDEAS

    1. Foster, Dean P., 1999. "A Proof of Calibration via Blackwell's Approachability Theorem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 73-78, October.
    2. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
    3. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    4. Chen, Xiaohong & White, Halbert, 1996. "Laws of Large Numbers for Hilbert Space-Valued Mixingales with Applications," Econometric Theory, Cambridge University Press, vol. 12(02), pages 284-304, June.
    5. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
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    More about this item


    rationalizability; curb set; rational behavior; algorithm; rationalizability.;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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