# Are Equivariant Equilibrium Approximators Beneficial?

arXiv: https://arxiv.org/abs/2301.11481 · HTML: https://mlsanity.com/paper/2301.11481/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 43 references that are in the map.
- First posted on arXiv 27 Jan 2023.

## Builds on (most cited first, 20 of 20)

- [A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning](https://mlsanity.com/paper/1711.00832/) (2017)
- [V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL](https://mlsanity.com/paper/2110.14555/) (2021)
- [Provably Strict Generalisation Benefit for Equivariant Models](https://mlsanity.com/paper/2102.10333/) (2021)
- [A Permutation-Equivariant Neural Network Architecture For Auction Design](https://mlsanity.com/paper/2003.01497/) (2020)
- [Computing Approximate Equilibria in Sequential Adversarial Games by Exploitability Descent](https://mlsanity.com/paper/1903.05614/) (2019)
- [Optimal-er Auctions through Attention](https://mlsanity.com/paper/2202.13110/) (2022)
- [Econometrics for Learning Agents](https://mlsanity.com/paper/1505.00720/) (2015)
- [What game are we playing? End-to-end learning in normal and extensive form games](https://mlsanity.com/paper/1805.02777/) (2018)
- [Multi-Agent Training beyond Zero-Sum with Correlated Equilibrium Meta-Solvers](https://mlsanity.com/paper/2106.09435/) (2021)
- [On the Complexity of Computing Markov Perfect Equilibrium in General-Sum Stochastic Games](https://mlsanity.com/paper/2109.01795/) (2021)
- [A Context-Integrated Transformer-Based Neural Network for Auction Design](https://mlsanity.com/paper/2201.12489/) (2022)
- [Contextual Games: Multi-Agent Learning with Side Information](https://mlsanity.com/paper/2107.06327/) (2021)
- [Meta-Learning in Games](https://mlsanity.com/paper/2209.14110/) (2022)
- [Turbocharging Solution Concepts: Solving NEs, CEs and CCEs with Neural Equilibrium Solvers](https://mlsanity.com/paper/2210.09257/) (2022)
- [Learning Utilities and Equilibria in Non-Truthful Auctions](https://mlsanity.com/paper/2007.01722/) (2020)
- [Simplex Neural Population Learning: Any-Mixture Bayes-Optimality in Symmetric Zero-sum Games](https://mlsanity.com/paper/2205.15879/) (2022)
- [Benefits of Permutation-Equivariance in Auction Mechanisms](https://mlsanity.com/paper/2210.05579/) (2022)
- [Exploitability Minimization in Games and Beyond](https://mlsanity.com/paper/2210.10207/) (2022)
- [A Polynomial-Time Algorithm for 1/3-Approximate Nash Equilibria in Bimatrix Games](https://mlsanity.com/paper/2204.11525/) (2022)
- [Is Nash Equilibrium Approximator Learnable?](https://mlsanity.com/paper/2108.07472/) (2021)

## Built on by (most cited first, 2 of 2)

- [A Scalable Neural Network for DSIC Affine Maximizer Auction Design](https://mlsanity.com/paper/2305.12162/) (2023)
- [Large-Scale Contextual Market Equilibrium Computation through Deep Learning](https://mlsanity.com/paper/2406.15459/) (2024)

## Abstract (arXiv)

Recently, remarkable progress has been made by approximating Nash equilibrium (NE), correlated equilibrium (CE), and coarse correlated equilibrium (CCE) through function approximation that trains a neural network to predict equilibria from game representations. Furthermore, equivariant architectures are widely adopted in designing such equilibrium approximators in normal-form games. In this paper, we theoretically characterize benefits and limitations of equivariant equilibrium approximators. For the benefits, we show that they enjoy better generalizability than general ones and can achieve better approximations when the payoff distribution is permutation-invariant. For the limitations, we discuss their drawbacks in terms of equilibrium selection and social welfare. Together, our results help to understand the role of equivariance in equilibrium approximators.