# 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} }

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…

## 20 Citations

Query Complexity of Approximate Equilibria in Anonymous Games

- Computer Science, EconomicsWINE
- 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

- Computer ScienceFOCS
- 2016

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 ScienceTheory 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

- Computer Science2016 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, MathematicsSAGT
- 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 ScienceACM 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)

- Economics2020 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

- EconomicsHardness 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, EconomicsJ. Comput. Syst. Sci.
- 2017

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