# The Query Complexity of Correlated Equilibria

arXiv: https://arxiv.org/abs/1305.4874 · HTML: https://mlsanity.com/paper/1305.4874/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2013.

## Built on by (most cited first, 5 of 5)

- [When Can We Learn General-Sum Markov Games with a Large Number of Players Sample-Efficiently?](https://mlsanity.com/paper/2110.04184/) (2021)
- [Fast swap regret minimization and applications to approximate correlated equilibria](https://mlsanity.com/paper/2310.19647/) (2023)
- [Towards Characterizing the First-order Query Complexity of Learning (Approximate) Nash Equilibria in Zero-sum Matrix Games](https://mlsanity.com/paper/2304.12768/) (2023)
- [Algorithmic Collusion and the Complexity of Information-Value-Free Equilibria](https://mlsanity.com/paper/2609.22757/) (2026)
- [An active learning method for solving competitive multi-agent decision-making and control problems](https://mlsanity.com/paper/2212.12561/) (2022)

## Abstract (arXiv)

We consider the complexity of finding a correlated equilibrium of an n-player game in a model that allows the algorithm to make queries on players' payoffs at pure strategy profiles. Randomized regret-based dynamics are known to yield an approximate correlated equilibrium efficiently, namely, in time that is polynomial in the number of players n. Here we show that both randomization and approximation are necessary: no efficient deterministic algorithm can reach even an approximate correlated equilibrium, and no efficient randomized algorithm can reach an exact correlated equilibrium. The results are obtained by bounding from below the number of payoff queries that are needed.