Linear-quadratic stochastic nonzero-sum differential games between graphon teams
Optimization and Control
2025-06-16 v1
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.
Cite
@article{arxiv.2506.11468,
title = {Linear-quadratic stochastic nonzero-sum differential games between graphon teams},
author = {De-xuan Xu and Zhun Gou and Nan-jing Huang},
journal= {arXiv preprint arXiv:2506.11468},
year = {2025}
}