@inproceedings{liu2024_nfgtransformer, title={NfgTransformer: Equivariant Representation Learning for Normal-form Games}, author={Siqi Liu and Luke Marris and Georgios Piliouras and Ian Gemp and Nicolas Heess}, booktitle={The Twelfth International Conference on Learning Representations}, year={2024}, url={https://openreview.net/forum?id=4YESQqIys7} } @misc{marris2023_equilibrium_invariant_embedding_2x2_arxiv, title={Equilibrium-Invariant Embedding, Metric Space, and Fundamental Set of 2×2 Normal-Form Games}, author={Luke Marris and Ian Gemp and Georgios Piliouras}, year={2023}, eprint={2304.09978}, archivePrefix={arXiv}, primaryClass={cs.GT}, url = {https://arxiv.org/abs/2304.09978}, } @article{bruns2015_names_for_games, author = {Bruns, Bryan Randolph}, title = {Names for Games: Locating 2 × 2 Games}, journal = {Games}, volume = {6}, year = {2015}, number = {4}, pages = {495--520}, url = {https://www.mdpi.com/2073-4336/6/4/495}, issn = {2073-4336}, abstract = {Prisoner’s Dilemma, Chicken, Stag Hunts, and other two-person two-move (2 × 2) models of strategic situations have played a central role in the development of game theory. The Robinson–Goforth topology of payoff swaps reveals a natural order in the payoff space of 2 × 2 games, visualized in their four-layer “periodic table” format that elegantly organizes the diversity of 2 × 2 games, showing relationships and potential transformations between neighboring games. This article presents additional visualizations of the topology, and a naming system for locating all 2 × 2 games as combinations of game payoff patterns from the symmetric ordinal 2 × 2 games. The symmetric ordinal games act as coordinates locating games in maps of the payoff space of 2 × 2 games, including not only asymmetric ordinal games and the complete set of games with ties, but also ordinal and normalized equivalents of all games with ratio or real-value payoffs. An efficient nomenclature can contribute to a systematic understanding of the diversity of elementary social situations; clarify relationships between social dilemmas and other joint preference structures; identify interesting games; show potential solutions available through transforming incentives; catalog the variety of models of 2 × 2 strategic situations available for experimentation, simulation, and analysis; and facilitate cumulative and comparative research in game theory.}, doi = {10.3390/g6040495} } @book{robinsonandgoforth2005_topology_of_2x2_games_book, author = {Robinson, David and Goforth, David}, year = {2005}, month = {01}, pages = {}, title = {The Topology of the 2x2 games: A New Periodic Table}, doi = {10.4324/9780203340271} } @book{goforth2005_periodic_table_of_games, author = {Goforth, David and Robinson, David}, year = {2005}, month = {01}, pages = {}, title = {Dynamic Periodic Table of the 2 × 2 Games: User's Reference and Manual}, } @article{borm1987_classification_of_2x2_games, title = "A classification of 2x2 bimatrix games", author = "P.E.M. Borm", note = "Pagination: 16", year = "1987", language = "English", volume = "29", pages = "69--84", journal = "Cahiers du Centre d'{\'E}tudes de Recherche Op{\'e}rationnelle", issn = "0008-9737", publisher = "Universit{\'e} libre de Bruxelles, Centre d'{\'e}tudes de recherche op{\'e}rationnelle", number = "1-2", }