A Nonzero-sum game with reinforcement learning under mean-variance framework

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<title>Nonzero-sum game with reinforcement learning under mean-variance framework</title>
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<namePart>Guo, Junyi</namePart>
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<abstract displayLabel="Summary">This paper examines a competitive setting in which two agents invest in a risk-free and a risky asset while considering both their own wealth and their wealth gap relative to each other. With market parameters partially or fully unknown, the problem is formulated as a nonzero-sum differential game within a reinforcement learning framework. Each agent seeks to optimize a Choquet-regularized, time-inconsistent mean-variance objective. Using dynamic programming, the authors derive a time-consistent Nash equilibrium in an incomplete market. Under a Gaussian mean-return assumption, they obtain an explicit analytical solution that enables the construction of a practical reinforcement learning algorithm. The algorithm shows uniform convergence, despite the absence of a traditional policy-improvement guarantee, and numerical experiments confirm its robustness and effectiveness</abstract>
<note type="statement of responsibility">Junyi Guo...[et al.]</note>
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<publisher>Belgium : ASTIN and AFIR Sections of the International Actuarial Association</publisher>
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<identifier type="issn">0515-0361</identifier>
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<text>19/01/2026 Volume 56 Issue 1 - January 2026 , p. 154 - 180</text>
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