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The Query Complexity of Correlated Equilibria

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  • Sergiu Hart

  • Noam Nisan

Abstract

We consider the complexity of finding a Correlated Equilibrium in an n-player game in a model that allows the algorithm to make queries for players' utilities at pure strategy profiles. Many randomized regret-matching dynamics are known to yield an approximate correlated equilibrium quickly: in time that is polynomial in the number of players, n, the number of strategies of each player, m, and the approximation error, 1/?. Here we show that both randomization and approximation are necessary: no efficient deterministic algorithm can reach even an approximate equilibrium and no efficient randomized algorithm can reach an exact equilibrium.

Suggested Citation

  • Sergiu Hart & Noam Nisan, 2013. "The Query Complexity of Correlated Equilibria," Discussion Paper Series dp647, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp647
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    Cited by:

    1. Forges, Françoise & Ray, Indrajit, 2024. "“Subjectivity and correlation in randomized strategies”: Back to the roots," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    2. Ayan Bhattacharya, 2019. "On Adaptive Heuristics that Converge to Correlated Equilibrium," Games, MDPI, vol. 10(1), pages 1-11, January.
    3. Bhaskar, Umang & Ligett, Katrina & Schulman, Leonard J. & Swamy, Chaitanya, 2019. "Achieving target equilibria in network routing games without knowing the latency functions," Games and Economic Behavior, Elsevier, vol. 118(C), pages 533-569.

    More about this item

    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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