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.

翻译：近期，通过函数近似方法（即训练神经网络从博弈表示中预测均衡）在近似纳什均衡、相关均衡和粗相关均衡方面取得了显著进展。此外，在正则形式博弈中设计此类均衡近似器时，等变架构被广泛采用。本文从理论上刻画了等变均衡近似器的优势与局限。在优势方面，我们证明其泛化能力优于普通近似器，且在收益分布满足置换不变性时能够实现更优近似。在局限方面，我们讨论了等变近似器在均衡选择和社会福利方面的缺陷。综合而言，本研究有助于理解等变性在均衡近似器中的作用。