Game, Set, Quantum: Parameterized Quantum Circuit for Correlated Equilibrium in Bayesian Games
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Quantum Physics arXiv:2606.03109 (quant-ph) [Submitted on 2 Jun 2026] Title:Game, Set, Quantum: Parameterized Quantum Circuit for Correlated Equilibrium in Bayesian Games Authors:Param Pathak, Vidhi Oad, Nouhaila Innan, Adarsh Ganesan, Muhammad Shafique View a PDF of the paper titled Game, Set, Quantum: Parameterized Quantum Circuit for Correlated Equilibrium in Bayesian Games, by Param Pathak and 3 other authors View PDF HTML (experimental) Abstract:Strategic decision-making among many agents under incomplete information is central to economics, security, and multi-agent artificial intelligence (AI). Computing equilibria in such settings is challenging because the joint type-action space grows exponentially with the number of players. In binary-type, binary-action Bayesian games, an explicit representation over type-action profiles requires O(22n) entries, making direct linear-programming (LP) formulations memory intensive at moderate player counts. We propose a hybrid quantum-classical framework for approximating Bayes correlated equilibrium using a parameterized quantum circuit (PQC). The PQC represents the conditional strategy distribution with O(nL) trainable parameters, where n is the number of players and L is the circuit depth; for the largest setting studied here, n = 10 and L = 2, this corresponds to 60 trainable angles. The circuit is trained by gradient-based regret minimization with a negative entropy regularizer and a curriculum schedule over player counts. On a poker-style Bayesian game with two to ten players, the proposed solver achieves lower mean clipped regret than MCCFR across all tested player counts and lower regret than DCFR up to eight players, while DCFR performs best at ten players. These results show that compact PQC parameterizations can provide a viable variational representation for approximate equilibrium computation, while highlighting the roles of ansatz expressivity, optimization strategy, and classical simulation cost. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.03109 [quant-ph] (or arXiv:2606.03109v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.03109 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Adarsh Venkataraman Ganesan [view email] [v1] Tue, 2 Jun 2026 03:52:16 UTC (1,503 KB) Full-text links: Access Paper: View a PDF of the paper titled Game, Set, Quantum: Parameterized Quantum Circuit for Correlated Equilibrium in Bayesian Games, by Param Pathak and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)