Learning Dynamic Games for Cooperative Iterative Tasks

We consider cooperative and iterative tasks involving multiple agents whose interactions are modeled as a dynamic game with shared constraints. We propose a general learning framework applicable to nonlinear and nonconvex dynamic games that uses previously executed feasible trajectories to construct a sampled joint safe set and player-specific cost-to-go functions. At each time step, the agents jointly select a previously sampled terminal state and a Generalized Nash equilibrium used to reach it. A new solution is adopted only if it satisfies a cooperative acceptance rule agreed upon by the players. The framework accommodates individual non-degradation requirements and selection criteria such as weighted costs and Nash bargaining. We show that the proposed framework guarantees recursive feasibility and characterize conditions under which each player's cost is non-increasing across iterations.