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arXiv · 2506.11468

Linear-quadratic stochastic nonzero-sum differential games between graphon teams

De-xuan Xu·Zhun Gou·Nan-jing Huang
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Abstract

We study a class of nonzero-sum stochastic differential games between two teams with agents in each team interacting through graphon aggregates. On the one hand, in each large population group, agents act together to optimize a common social cost function. On the other hand, these two groups compete with each other, forming a Nash game between two graphon teams. We note that the original problem can be equivalently formulated as an infinite-dimensional two-agent Nash game. Applying the dynamic programming approach, we obtain a set of coupled operator-valued Riccati-type equations. By proving the existence of solutions to the equations mentioned above, we obtain a Nash equilibrium for the two teams.

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De-xuan Xu, Zhun Gou, Nan-jing Huang. 2025-06-13. Linear-quadratic stochastic nonzero-sum differential games between graphon teams. https://arxiv.org/abs/2506.11468

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