Cooperative attack-defense evolution of large-scale agents: a multi-population high-dimensional mean-field game approach

The traditional optimization and control technologies deal with the dynamic interactions between individuals separately, with the increase in the agents' number, the modeling process of cooperative attack-defense problems tends to be complex, and the difficulty of solving the optimal strategy will increase significantly. Moreover, to carry out more accurate real-time control of agents, the state variables used to characterize their kinematics are usually high-dimensional. To overcome these challenges, we formulate the cooperative attack-defense evolution of large-scale agents as a multi-population high-dimensional stochastic mean-field game (MPHD-MFG). Numerical methods for MPHD-MFGs are practically non-existent, because, the heterogeneity of the multi-population model increases the complexity of sequential games, and grid-based spatial discretization leads to dimension explosion. Thus, we propose a generative adversarial network-based method, where we use a coupled alternating neural network composed of multiple generators and multiple discriminators, to tractably solve MPHD-MFGs. Simulation experiments are carried out for various attack-defense scenarios, the results verify the feasibility and effectiveness of our proposed model and algorithm.