Learning in constrained stochastic dynamic potential games

We extend earlier works on continuous potential games to the most general case: stochastic time varying environment, stochastic rewards, non-reduced form and constrained state-action sets. We provide conditions for a Markov Nash equilibrium (MNE) of the game to be equivalent to the solution of a single control problem. Then, we address the problem of learning this MNE when the reward and state transition models are unknown. We follow a reinforcement learning approach and extend previous algorithms for working with constrained state-action subsets of real vector spaces. As an application example, we simulate a network flow optimization model, in which the relays have batteries that deplete with a random factor. The results obtained with the proposed framework are close to optimal.