{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/real-world-games-look-like-spinning-tops","title":"Real World Games Look Like Spinning Tops","arxiv_id":"2004.09468","date":"2020-04-20","proceeding":"NeurIPS 2020 12","authors":["Wojciech Marian Czarnecki","Gauthier Gidel","Brendan Tracey","Karl Tuyls","Shayegan Omidshafiei","David Balduzzi","Max Jaderberg"],"abstract":"This paper investigates the geometrical properties of real world games (e.g. Tic-Tac-Toe, Go, StarCraft II). We hypothesise that their geometrical structure resemble a spinning top, with the upright axis representing transitive strength, and the radial axis, which corresponds to the number of cycles that exist at a particular transitive strength, representing the non-transitive dimension. We prove the existence of this geometry for a wide class of real world games, exposing their temporal nature. Additionally, we show that this unique structure also has consequences for learning - it clarifies why populations of strategies are necessary for training of agents, and how population size relates to the structure of the game. Finally, we empirically validate these claims by using a selection of nine real world two-player zero-sum symmetric games, showing 1) the spinning top structure is revealed and can be easily re-constructed by using a new method of Nash clustering to measure the interaction between transitive and cyclical strategy behaviour, and 2) the effect that population size has on the convergence in these games.","url_abs":"https://arxiv.org/abs/2004.09468v2","url_pdf":"https://arxiv.org/pdf/2004.09468v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"real-world-games-look-like-spinning-tops","repo_url":"https://github.com/sjtu-marl/bd_rd_psro","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"starcraft","task_name":"Starcraft"},{"task_slug":"starcraft-ii","task_name":"Starcraft II"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2004.09468","atlas_url":"https://app.syntology.ai/?focus=2004.09468","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}