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Refined best-response correspondence and dynamics

Author

Listed:
  • Dieter Balkenborg

    (Department of Economics, University of Exeter)

  • Josef Hofbauer

    (Department of Mathematics, University of Vienna)

  • Christoph Kuzmics

    (Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University)

Abstract

We characterize the smallest faces of the polyhedron of strategy profiles that could possibly be made asymptotically stable under some reasonable deterministic dynamics. These faces are Kalai and Samet's (1984) persistent retracts and are spanned by Basu and Weibull's (1991) CURB sets based on a natural (and, in a well-defined sense, minimal) refinement of the best-reply correspondence. We show that such a correspondence satisfying basic properties such as existence, upper hemi-continuity, and convex-valuedness exists and is unique in most games. We introduce a notion of rationalizability based on this correspondence and its relation to other such concepts. We study its fixed-points and their relations to equilibrium refinements. We find, for instance, that a fixed point of the refined best reply correspondence in the agent normal form of any extensive form game constitutes a perfect Bayesian equilibrium, which is weak perfect Bayesian in every subgame. Finally, we study the index of its fixed point components.

Suggested Citation

  • Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2008. "Refined best-response correspondence and dynamics," Discussion Papers 0806, University of Exeter, Department of Economics.
    • Handle: RePEc:exe:wpaper:0806
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    Citations

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    Cited by:

    1. Hans Carlsson & Philipp Christoph Wichardt, 2019. "Strict Incentives and Strategic Uncertainty," CESifo Working Paper Series 7715, CESifo.
    2. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2023. "Strategy sets closed under payoff sampling," Games and Economic Behavior, Elsevier, vol. 138(C), pages 126-142.
    3. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2015. "The refined best-response correspondence in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 165-193, February.
    4. Peter Wikman, 2022. "Nash blocks," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 29-51, March.
    5. Balkenborg, Dieter, 2018. "Rationalizability and logical inference," Games and Economic Behavior, Elsevier, vol. 110(C), pages 248-257.
    6. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. Christopher Kah & Markus Walzl, 2015. "Stochastic Stability in a Learning Dynamic with Best Response to Noisy Play," Working Papers 2015-15, Faculty of Economics and Statistics, Universität Innsbruck.
    8. repec:grz:wpaper:2016-11 is not listed on IDEAS
    9. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2009. "The Refined Best-Response Correspondence and Backward Induction," Levine's Working Paper Archive 814577000000000248, David K. Levine.
    10. Balkenborg Dieter & Kuzmics Christoph & Hofbauer Josef, 2019. "The Refined Best Reply Correspondence and Backward Induction," German Economic Review, De Gruyter, vol. 20(1), pages 52-66, February.
    11. Dai Zusai, 2018. "Tempered best response dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 1-34, March.
    12. Xu, Zibo, 2016. "Convergence of best-response dynamics in extensive-form games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 21-54.
    13. Leslie, David S. & Perkins, Steven & Xu, Zibo, 2020. "Best-response dynamics in zero-sum stochastic games," Journal of Economic Theory, Elsevier, vol. 189(C).

    More about this item

    Keywords

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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