Factorization of Dynamic Games over Spatio-Temporal Resources

Dynamic games feature a state-space complexity that scales superlinearly with the number of players. This makes this class of games often intractable even for a handful of players. We introduce the factorization process of dynamic games as a transformation leveraging the independence of players at equilibrium to build a leaner game graph. When applicable, it yields fewer nodes, fewer players per game node, hence much faster solutions. While for the general case checking for independence of players requires to solve the game itself, we observe that for dynamic games in the robotic domain there exist exact heuristics based on the spatio-temporal occupancy of the individual players. We validate our findings in realistic autonomous driving scenarios showing that already for a 4-player intersection we have a reduction of game nodes and solving time close to 99%.