Are Equivariant Equilibrium Approximators Beneficial?

TL;DR

This paper analyzes the advantages and limitations of using equivariant neural network architectures to approximate Nash and related equilibria in game theory, highlighting their improved generalizability and potential drawbacks.

Contribution

It provides a theoretical characterization of when equivariant equilibrium approximators outperform general ones and discusses their limitations in equilibrium selection and social welfare.

Findings

Equivariant approximators have better generalizability.

They achieve superior approximations with permutation-invariant payoffs.

Limitations include issues in equilibrium selection and social welfare.

Abstract

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.