On the Equivalence of Zero-Sum Games and Conic Programs

[2302.03066] On the Equivalence of Zero-Sum Games and Conic Programs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2302.03066 (math) [Submitted on 6 Feb 2023 ( v1 ), last revised 11 Apr 2026 (this version, v5)] Title: On the Equivalence of Zero-Sum Games and Conic Programs Authors: Nikos Dimou View a PDF of the paper titled On the Equivalence of Zero-Sum Games and Conic Programs, by Nikos Dimou View PDF HTML (experimental) Abstract: We prove the almost equivalence of the minimax theorem and the strong duality theorem for a large class of games and conic programs. The previous fundamental results on the equivalence of linear programming and two-player zero-sum games with simplex-strategy sets are extended to Banach spaces, and a comprehensive framework unifying two-player zero-sum games and conic linear programs is established. Specifically, we show that for every zero-sum game with a bilinear payoff function and strategy sets that represent bases of convex cones, the minimax equality holds and its game value and Nash equilibria can be found by solving a primal-dual pair of conic programs. Conversely, the minimax theorem for the same class of games "almost always" implies strong duality of conic linear programming. In fact, we give a game-dependent characterization of strict feasibility, and show that minimax is equivalent to a generalized version of Ville's theorem of the alternative. Several well-established game classes are embedded in the introduced model, including (i) semi-infinite, (ii) semidefinite, (iii) quantum, (iv) time-dependent, and (v) polynomial games, as well as (vi) the mixed extension of any continuous game with compact strategy sets. Comments: Complete paper version of an early draft; several Sections were added and various proofs have been shortened Subjects: Optimization and Control (math.OC) ; Computer Science and Game Theory (cs.GT) MSC classes: 90C45, 90C46, 91A05, 46N10 Cite as: arXiv:2302.03066 [math.OC] (or arXiv:2302.03066v5 [math.OC] for this version) https://doi.org/10.48550/arXiv.2302.03066 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1287/moor.2025.0926 Focus to learn more DOI(s) linking to related resources Submission history From: Nikos Dimou [ view email ] [v1] Mon, 6 Feb 2023 19:08:53 UTC (24 KB) [v2] Sun, 19 Mar 2023 19:59:27 UTC (26 KB) [v3] Wed, 5 Jun 2024 15:48:11 UTC (48 KB) [v4] Sat, 24 Aug 2024 02:56:03 UTC (52 KB) [v5] Sat, 11 Apr 2026 21:33:30 UTC (44 KB) Full-text links: Access Paper: View a PDF of the paper titled On the Equivalence of Zero-Sum Games and Conic Programs, by Nikos Dimou View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2023-02 Change to browse by: cs cs.GT math References & Citations NASA ADS Google 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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