等变均衡近似器是否有益？
Are Equivariant Equilibrium Approximators Beneficial?
AI总结：
本文理论分析标准式博弈中等变均衡近似器的优劣，证明其在置换不变收益分布下泛化与近似更优，同时指出均衡选择和社会福利方面的局限。
摘要：
近来，通过函数近似来近似 Nash 均衡（NE）、相关均衡（CE）和粗相关均衡（CCE）已取得显著进展；这类方法训练神经网络，根据博弈表示预测均衡。此外，等变架构被广泛用于设计标准式博弈中的此类均衡近似器。本文从理论上刻画等变均衡近似器的收益与局限。在收益方面，我们证明，当收益分布具有置换不变性时，它们比一般近似器具有更好的泛化能力，并能实现更好的近似。在局限方面，我们讨论其在均衡选择和社会福利方面的缺陷。总体而言，我们的结果有助于理解等变性在均衡近似器中的作用。
英文摘要：
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.
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