NfgTransformer: Equivariant Representation Learning for Normal-form Games
Siqi Liu, Luke Marris, Georgios Piliouras, Ian Gemp, Nicolas Heess
Abstract
Normal-form games (NFGs) are the fundamental model of strategic interaction. We study their representation using neural networks. We describe the inherent equivariance of NFGs -- any permutation of strategies describes an equivalent game -- as well as the challenges this poses for representation learning. We then propose the NfgTransformer architecture that leverages this equivariance, leading to state-of-the-art performance in a range of game-theoretic tasks including equilibrium-solving, deviation gain estimation and ranking, with a common approach to NFG representation. We show that the resulting model is interpretable and versatile, paving the way towards deep learning systems capable of game-theoretic reasoning when interacting with humans and with each other.
Ask about this paper
Your agent reads all of it.
Lune indexed this paper to the last equation, along with the top-tier papers that cite it. Ask a question and the answer quotes them.
Your agent calls
Luneget_paper_fulltext
Free to start. No credit card required.
Terminal
Install the CLIlune papers fulltext a0c8269a-671d-4116-b1d7-73f3201c93bcCited by top-tier papers4
- Computing Game Symmetries and Equilibria That Respect ThemEmanuel Tewolde, Brian Hu Zhang, Caspar Oesterheld, Tuomas Sandholm et al.AAAI 2025 · 6 citations
- Deep Incentive Design with Differentiable Equilibrium BlocksVinzenz Thoma, Georgios Piliouras, Luke MarrisICML 2026
- Tree-Based Stochastic Optimization for Solving Large-Scale Urban Network Security GamesShuxin Zhuang, Linjian Meng, Shuxin Li, Minming Li et al.AAAI 2026
- Reducing Variance of Stochastic Optimization for Approximating Nash Equilibria in Normal-Form GamesLinjian Meng, Wubing Chen, Wenbin Li, Tianpei Yang et al.ICML 2025
Builds on7
- An Image is Worth 16x16 Words: Transformers for Image Recognition at ScaleAlexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn et al.ICLR 2021 · 21,477 citations
- Perceiver: General Perception with Iterative AttentionAndrew Jaegle, Felix Gimeno, Andy Brock, Oriol Vinyals et al.ICML 2021 · 1,399 citations
- No-Regret Learning and Mixed Nash Equilibria: They Do Not MixEmmanouil V. Vlatakis-Gkaragkounis, Lampros Flokas, Thanasis Lianeas, Panayotis Mertikopoulos et al.NeurIPS 2020 · 100 citations
- Neural Auto-Curricula in Two-Player Zero-Sum GamesXidong Feng, Oliver Slumbers, Ziyu Wan, Bo Liu et al.NeurIPS 2021 · 40 citations
- Turbocharging Solution Concepts: Solving NEs, CEs and CCEs with Neural Equilibrium SolversLuke Marris, Ian Gemp, Thomas Anthony, Andrea Tacchetti et al.NeurIPS 2022 · 22 citations
Related papers
- Learning to Infer Structures of Network GamesEmanuele Rossi, Federico Monti, Yan Leng, Michael M. Bronstein et al.ICML 2022 · 9 citations
- Are Equivariant Equilibrium Approximators Beneficial?Zhijian Duan, Yunxuan Ma, Xiaotie DengICML 2023 · 4 citations
- An Efficient Deep Reinforcement Learning Algorithm for Solving Imperfect Information Extensive-Form GamesLinjian Meng, Zhenxing Ge, Pinzhuo Tian, Bo An et al.AAAI 2023 · 8 citations
- Learning Game-Theoretic Models of Multiagent Trajectories Using Implicit LayersPhilipp Geiger, Christoph-Nikolas StraehleAAAI 2021 · 31 citations
- Benefits of Permutation-Equivariance in Auction MechanismsTian Qin, Fengxiang He, Dingfeng Shi, Wenbing Huang et al.NeurIPS 2022 · 13 citations
