Are Equivariant Equilibrium Approximators Beneficial?

Zhijian Duan, Yunxuan Ma, Xiaotie Deng
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:8747-8778, 2023.

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 the 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-duan23d, title = {Are Equivariant Equilibrium Approximators Beneficial?}, author = {Duan, Zhijian and Ma, Yunxuan and Deng, Xiaotie}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {8747--8778}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/duan23d/duan23d.pdf}, url = {https://proceedings.mlr.press/v202/duan23d.html}, 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 the 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.} }
Endnote
%0 Conference Paper %T Are Equivariant Equilibrium Approximators Beneficial? %A Zhijian Duan %A Yunxuan Ma %A Xiaotie Deng %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-duan23d %I PMLR %P 8747--8778 %U https://proceedings.mlr.press/v202/duan23d.html %V 202 %X 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 the 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.
APA
Duan, Z., Ma, Y. & Deng, X.. (2023). Are Equivariant Equilibrium Approximators Beneficial?. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:8747-8778 Available from https://proceedings.mlr.press/v202/duan23d.html.

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