Stochastic Differential Games and Decentralized Control - Elm Jonsson, Benjamin; Fazlija, Bekir (My University, 2025)
Multi-agent stochastic control games naturally give rise to coupled forward backward stochastic differential equations (FBSDE) for each agent. In such cases, dependencies exist both between the forward and backward equations and across agents, resulting in a highly non-trivial system to solve. In this thesis, a novel solution algorithm for such systems is presented, that is more robust compared to the existing Deep Fictitious Play method. The algorithm presented has been validated through several numerical examples. An analytical solution for linear–quadratic–Gaussian differential games is derived to validate the algorithm for problems where the Deep Fictitious Play algorithm has been shown to fail. This demonstrates the improved capabilities compared to the algorithms in the literature. In addition, a complex numerical example is designed that models a heterogeneous stochastic control game, which describes a swarm of drones following a predefined trajectory.
Keywords: Stochastic differential equation, Forward backward differential equation, Game theory, Stochastic control, Fictitious play, Multi-agent games.