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The query complexity of correlated equilibria

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  • Hart, Sergiu
  • Nisan, Noam

Abstract

We consider the complexity of finding a correlated equilibrium of an n-player game in a model that allows the algorithm to make queries on players' payoffs at pure strategy profiles. Randomized regret-based dynamics are known to yield an approximate correlated equilibrium efficiently, namely, in time that is polynomial in the number of players n. Here we show that both randomization and approximation are necessary: no efficient deterministic algorithm can reach even an approximate correlated equilibrium, and no efficient randomized algorithm can reach an exact correlated equilibrium. The results are obtained by bounding from below the number of payoff queries that are needed.

Suggested Citation

  • Hart, Sergiu & Nisan, Noam, 2018. "The query complexity of correlated equilibria," Games and Economic Behavior, Elsevier, vol. 108(C), pages 401-410.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:401-410
    DOI: 10.1016/j.geb.2016.11.003
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    References listed on IDEAS

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    1. Sergiu Hart & Andreu Mas-Colell, 2013. "Stochastic Uncoupled Dynamics And Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 8, pages 165-189, World Scientific Publishing Co. Pte. Ltd..
    2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    3. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    4. Sergiu Hart & Andreu Mas-Colell, 2013. "A General Class Of Adaptive Strategies," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 3, pages 47-76, World Scientific Publishing Co. Pte. Ltd..
    5. Sergiu Hart & Yishay Mansour, 2013. "How Long To Equilibrium? The Communication Complexity Of Uncoupled Equilibrium Procedures," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 10, pages 215-249, World Scientific Publishing Co. Pte. Ltd..
    6. Sergiu Hart & Andreu Mas-Colell, 2013. "Simple Adaptive Strategies:From Regret-Matching to Uncoupled Dynamics," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8408, June.
    7. Jiang, Albert Xin & Leyton-Brown, Kevin, 2015. "Polynomial-time computation of exact correlated equilibrium in compact games," Games and Economic Behavior, Elsevier, vol. 91(C), pages 347-359.
    8. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
    9. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    10. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
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    Cited by:

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    More about this item

    Keywords

    Correlated equilibria; Complexity; Query; Approximate equilibria; Regret-based; Randomized algorithm; Query complexity;
    All these keywords.

    JEL classification:

    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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