{"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/permissible-extensions-of-classical-to","title":"Permissible extensions of classical to quantum games combining three strategies","arxiv_id":"2404.06196","date":"2024-04-09","proceeding":null,"authors":["Piotr Frąckiewicz","Marek Szopa"],"abstract":"We study the extension of classical games to the quantum domain, generated by the addition of one unitary strategy to two classical strategies of each player. The conditions that need to be met by unitary operations to ensure that the extended game is invariant with respect to the isomorphic transformations of the input game are determined. It has been shown that there are three types of these extensions, two of them are purely quantum. On the other hand, it has been demonstrated that the extensions of two versions of the same classical game by a unitary operator that does not meet these conditions may result in quantum games that are non-equivalent, e.g. having different Nash equilibria. We use the obtained results to extend the classical Prisoner's Dilemma game to a quantum game that has a unique Nash equilibrium closer to Pareto-optimal solutions than the original one.","url_abs":"https://arxiv.org/abs/2404.06196v1","url_pdf":"https://arxiv.org/pdf/2404.06196v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"permissible-extensions-of-classical-to","repo_url":"https://github.com/k-grzanka/qegs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}