# Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games

@article{Chen2017WellSupportedVA,
title={Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games},
author={Xi Chen and Y. Cheng and Bo Tang},
journal={ArXiv},
year={2017},
volume={abs/1511.00785}
}
• Published 3 November 2015
• Computer Science
• ArXiv
We study the randomized query complexity of approximate Nash equilibria (ANE) in large games. We prove 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. For the stronger solution concept of well-supported Nash equilibria (WSNE), Babichenko previously gave an exponential $2^{\Omega(n)}$ lower bound for the randomized query complexity of $\epsilon$-WSNE, for…
Query Complexity of Approximate Equilibria in Anonymous Games
• Computer Science, Economics
WINE
• 2015
It is proved that $$\varOmega n \log {n}$$ payoffs must be queried in order to find any $$epsilon$$-well-supported Nash equilibrium, even by randomized algorithms, which is the first one to obtain an inverse polynomial approximation in poly-time.
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
Logarithmic Query Complexity for Approximate Nash Computation in Large Games
• Economics, Computer Science
Theory of Computing Systems
• 2018
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
• 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
Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games
• Economics, Mathematics
SAGT
• 2021
This work develops a query-efficient reduction from more general games to Lipschitz games, and provides an exponential lower bound on the deterministic query complexity of finding -approximate correlated equilibria of n-player, m-action, λ-Lipschitzer games for strong values of , motivating the consideration of explicitly randomized algorithms in the above results.
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.
2 5 D ec 2 01 7 The Query Complexity of Correlated Equilibria ∗ †
• Computer Science
• 2018
It is shown that both randomization and approximation are necessary: no efficient deterministic algorithm can reach even an approximate correlated equilibrium of an n-player game in a model that allows the algorithm to make queries on players’ payoffs at pure strategy profiles.
Communication complexity of Nash equilibrium in potential games (extended abstract)
• Economics
2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
• 2020
These are the first results to demonstrate hardness in any model of (possibly mixed) Nash equilibrium in potential games.
Hardness of Approximation Between P and NP
• A. Rubinstein
• Economics
Hardness of Approximation Between P and NP
• 2017
This book provides strong evidence that even finding an approximate Nash equilibrium is intractable, and proves several intractability theorems for different settings (two-player games and many- player games) and models (computational complexity, query complexity, and communication complexity).
Query complexity of approximate equilibria in anonymous games
• Computer Science, Economics
J. Comput. Syst. Sci.
• 2017

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