Towards Equilibrium Coordination With Stein Variational Game

Differential Dynamic Games (DDG) often admit non-unique and, in some cases, an infinite number of Nash Equilibria (NE). Miscoordination among agents in selecting a specific Nash Equilibrium can result in cost inefficiencies and compromise any stabilizing properties of these equilibria. In the case of Generalized Nash Equilibria (GNE), such miscoordination can lead to constraint violations, potentially causing catastrophic outcomes, such as collisions in practical applications. To address the equilibrium coordination problem, we propose a novel framework for estimating and selecting equilibria in a DDG. Our method utilizes a diffusion process to model the distribution of Nash Equilibria in a DDG, constructed through a sequence of mappings defined by Stein Variational Gradient Descent (SVGD). This distribution serves as a prior belief over the non-ego agents' equilibrium choices, which is dynamically refined using Bayesian inference as the game evolves. We validate the proposed approach in an autonomous vehicle traffic trajectory planning problem, demonstrating its effectiveness in environments where agents operate without explicit communication regarding their chosen Nash Equilibria.