Finite-Agent Stochastic Differential Games on Large Graphs: II. Graph-Based Architectures

תקציר מקורי באנגליתarXiv:2509.12484v2 Announce Type: replace Abstract: 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 i