# The Query Complexity of Correlated Equilibria

@article{Hart2018TheQC,
title={The Query Complexity of Correlated Equilibria},
author={Sergiu Hart and Noam Nisan},
journal={Games Econ. Behav.},
year={2018},
volume={108},
pages={401-410}
}
• Published 21 May 2013
• Economics
• Games Econ. Behav.
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A multi-armed bandit model is introduced to this problem due to its ability to find the best arm efficiently among random arms and two algorithms for this problem are proposed—LUCB-G based on the confidence bounds and a racing algorithm based on successive action elimination.
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This talk mostly focuses on the paper Fearnley et al. (Learning equilibria of games via payoff queries), which is a relatively recent line of work, which is reviewed here.
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Theory of Computing Systems
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A randomised algorithm is presented that achieves ε approaching 18$\frac {1}{8}$ for 2-strategy games in a completely uncoupled setting, where each player observes her own payoff to a query, and adjusts her behaviour independently of other players’ payoffs/actions.
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We prove that there exists a constant e > 0 such that, assuming the Exponential Time Hypothesis for PPAD, computing an e-approximate Nash equilibrium in a two-player (n × n) game requires
Settling the Complexity of Computing Approximate Two-Player Nash Equilibria
• A. Rubinstein
• Computer Science
2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
• 2016
We prove that there exists a constant ε > 0 such that, assuming the Exponential Time Hypothesis for PPAD, computing an ε-approximate Nash equilibrium in a two-player (n × n) game requires
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The survey provides a high-level idea of the techniques that are utilized to deduce recently developed lower bounds on Nash equilibria.
Finding Approximate Nash Equilibria of Bimatrix Games via Payoff Queries
• Economics, Computer Science
ACM Trans. Economics and Comput.
• 2016
It is shown that randomized algorithms require Ω(k2) payoff queries in order to find an ϵ-Nash equilibrium with ϵ < 1/4k, even in zero-one constant-sum games, which rules out query-efficient randomized algorithms for finding exact Nash equilibria.

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