Finite-Agent Stochastic Differential Games on Large Graphs: II. Graph-Based Architectures
This addresses graph-structured multi-agent systems in fields like finance and robotics, offering an incremental improvement in efficiency and interpretability for existing game solvers.
The paper tackles computing Nash equilibria in stochastic differential games on graphs by proposing a Non-Trainable Modification (NTM) neural network architecture that imposes graph-guided sparsification, achieving performance comparable to fully trainable methods with improved computational efficiency.
We propose a novel neural network architecture, called Non-Trainable Modification (NTM), for computing Nash equilibria in stochastic differential games (SDGs) on graphs. These games model a broad class of graph-structured multi-agent systems arising in finance, robotics, energy, and social dynamics, where agents interact locally under uncertainty. The NTM architecture imposes a graph-guided sparsification on feedforward neural networks, embedding fixed, non-trainable components aligned with the underlying graph topology. This design enhances interpretability and stability, while significantly reducing the number of trainable parameters in large-scale, sparse settings. We theoretically establish a universal approximation property for NTM in static games on graphs and numerically validate its expressivity and robustness through supervised learning tasks. Building on this foundation, we incorporate NTM into two state-of-the-art game solvers, Direct Parameterization and Deep BSDE, yielding their sparse variants (NTM-DP and NTM-DBSDE). Numerical experiments on three SDGs across various graph structures demonstrate that NTM-based methods achieve performance comparable to their fully trainable counterparts, while offering improved computational efficiency.