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}
}
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28 Citations
Highly Influential Citations
2
Background Citations
12
Methods Citations
2
Results Citations
1

28 Citations

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Citation Type

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Communication complexity of approximate Nash equilibria
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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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TLDR
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.
Settling the Complexity of Computing Approximate Two-Player Nash Equilibria
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
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  • 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…
Informational bounds on equilibria (a survey)
TLDR
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
TLDR
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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References

SHOWING 1-10 OF 36 REFERENCES
Query Complexity of Correlated Equilibrium
TLDR
A query model in which an n-player game is specified via a black box that returns players' utilities at pure action profiles is considered, establishing that in order to compute a correlated equilibrium, any deterministic algorithm must query the black box an exponential number of times.
Query complexity of approximate nash equilibria
TLDR
It is shown that even for constant ε, the query complexity of an ε-well-supported Nash equilibrium is exponential in n, which means that the Nash equilibrium of a large number of players n and a constant number of actions m is linear in n.
Learning equilibria of games via payoff queries
TLDR
This work studies a corresponding computational learning model, and the query complexity of learning equilibria for various classes of games, and has the stronger result that an equilibrium can be identified while only learning a small fraction of the cost values.
Empirical Distribution of Equilibrium Play and Its Testing Application
TLDR
It is shown that in any n -player, m -action normal-form game, the existence of approximate equilibrium with support-size polylogarithmic in n and m is shown, whereas the previously best-known upper bounds were polynomial in n.
A simple adaptive procedure leading to correlated equilibrium
We propose a new and simple adaptive procedure for playing a game: ‘‘regret-matching.’’ In this procedure, players may depart from their current play with probabilities that are proportional to…
Polynomial computation of exact correlated equilibrium in compact games
TLDR
It is shown that the Ellipsoid Against Hope algorithm can be modified to compute an exact correlated equilibrium, and can be understood as a derandomization of Papadimitriou and Roughgarden's original separation oracle via the method of conditional expectations.
How long to equilibrium? The communication complexity of uncoupled equilibrium procedures
Simple strategies for large zero-sum games with applications to complexity theory
TLDR
An elementary proof that each player of a zero-sum matrix game has a near-optimal mixed strategy that chooses uniformly at random from a multiset of pure strategies of size logarithmic in the number ofpure strategies available to the opponent.
A General Class of Adaptive Strategies
We exhibit and characterize an entire class of simple adaptive strategies, in the repeated play of a game, having the Hannan-consistency property: In the long-run, the player is guaranteed an average…
Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games
TLDR
It is proved that, for some constant $\epsilon>0$, any randomized oracle algorithm that computes an $\epSilon$-ANE in a binary-action, $n$-player game must make $2^{\Omega(n/\log n)}$ payoff queries.
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