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Finding all minimal curb sets

Author

Listed:
  • Max Klimm

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

  • Jörgen Weibull

    (SSE - Department of Economics - SSE - Stockholm School of Economics, X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique)

Abstract

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
    Note: View the original document on HAL open archive server: https://hal.science/hal-00442118
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    Cited by:

    1. Juang, W-T. & Sabourian, H., 2021. "Rules and Mutation - A Theory of How Efficiency and Rawlsian Egalitarianism/Symmetry May Emerge," Cambridge Working Papers in Economics 2101, Faculty of Economics, University of Cambridge.

    More about this item

    Keywords

    curb set; rational behavior; algorithm; rationalizability.; rationalizability;
    All these keywords.

    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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