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

• URL: http://arxiv.org/abs/2509.12484v1
• Date: Mon, 15 Sep 2025 22:11:56 GMT
• Title: Finite-Agent Stochastic Differential Games on Large Graphs: II. Graph-Based Architectures
• Authors: Ruimeng Hu, Jihao Long, Haosheng Zhou,
• Abstract summary: We propose a novel neural network architecture, called Non-Trainable Modification (NTM), for computing Nash equilibria in differential games on graphs.<n>NTM imposes a graph-guided sparsification on feedforward neural networks, embedding fixed, non-trainable components aligned with the underlying graph topology.
• Score: 2.58713822033329
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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