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

TL;DR

This paper investigates stochastic differential games between two large teams with agents interacting through graphon structures, deriving Riccati equations to find Nash equilibria in an infinite-dimensional setting.

Contribution

It introduces a novel framework for nonzero-sum differential games between graphon-based teams and derives Riccati equations to characterize Nash equilibria.

Findings

Existence of solutions to Riccati-type equations established.

Nash equilibrium characterized for the graphon team game.

Framework extends to infinite-dimensional two-agent Nash games.

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.