Coupled Alternating Neural Networks for Solving Multi-Population High-Dimensional Mean-Field Games with Stochasticity

Multi-population mean-field game is a critical subclass of mean-field games (MFGs). It is a theoretically feasible multi-agent model for simulating and analyzing the game between multiple heterogeneous populations of interacting massive agents. Due to the factors of game complexity, dimensionality disaster and disturbances should be taken into account simultaneously, how to solve the multi-population high-dimensional stochastic MFG problem is faced with great challenges. We present CA-Net, a coupled alternating neural network approach for tractably solving multi-population high-dimensional MFGs in the stochastic case. First, we provide a universal modeling framework for large-scale heterogeneous multi-agent game systems, which is strictly expressed as a multi-population MFG problem. Next, we generalize the potential variational primal-dual structure that MFGs exhibit, then phrase the multi-population MFG problem as a convex-concave saddle-point problem. Last but not least, we design a generative adversarial network (GAN) with multiple generators and multiple discriminators—the solving network, which parameterizes the value functions and the density functions of multiple populations by two sets of neural networks, respectively. Moreover, numerical experiments demonstrate the feasibility and effectiveness of our approach.