Quantum game theory for 2 2 games: a mathematical framework
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Quantum Physics arXiv:2605.15747 (quant-ph) [Submitted on 15 May 2026] Title:Quantum game theory for 2 2 games: a mathematical framework Authors:Gloria Ferraris, Veronica Umanità View a PDF of the paper titled Quantum game theory for 2 2 games: a mathematical framework, by Gloria Ferraris and Veronica Umanit\`a View PDF HTML (experimental) Abstract:We develop a rigorous mathematical framework for quantum game theory applied to static 2x2 games, extending classical concepts to the quantum setting where players may employ arbitrary unitary operations (pure strategies) or probability measures over the continuous group SU(2) (mixed strategies). The Eisert-Wilkens-Lewenstein protocol is introduced as the standard implementation of quantum 2x2 games. We prove the existence of Nash equilibria for continuous quantum mixed strategies via a fixed-point argument, generalising the classical Nash theorem to the quantum case. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2605.15747 [quant-ph] (or arXiv:2605.15747v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.15747 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Veronica Umanità [view email] [v1] Fri, 15 May 2026 09:05:39 UTC (16 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum game theory for 2 2 games: a mathematical framework, by Gloria Ferraris and Veronica Umanit\`aView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)