2025/06/13 by Xu, De-xuan, Gou, Zhun, Huang, Nan-jing
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2506.11468
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.