Learning Dynamic Games for Cooperative Iterative Tasks

This paper studies feedback Nash equilibrium (FBNE) seeking for multi-agent trajectory planning in nonlinear dynamical systems with unknown agents' objectives and state-dependent inter-agent coupling. While dynamic game theory provides a principled framework for such problems, existing approaches typically assume fully rational agents with known objectives or rely on fixed regularization, limiting their ability to capture bounded rationality and spatially varying interaction intensity in safety-critical settings. To this end, we propose a KL-regularized dynamic game with a state-dependent weight that adaptively balances optimality and behavioral priors. To infer unknown cost parameters from demonstrated behaviors, we develop a context-aware inverse game module based on maximum-entropy inverse reinforcement learning with physics-informed regularization, ensuring structural consistency with the forward game. We establish per-iteration well-posedness of the regularized local game and show that the adaptive weighting function remains Lipschitz continuous under bounded nominal-trajectory updates. Numerical simulations and multi-robot experiments on cooperative navigation and merging scenarios validate the effectiveness of the proposed framework.

Cooperation emergence is a central problem in multi-agent systems because decentralized agents must coordinate while adapting to the changing behavior of others. Evolutionary game theory identifies strategically stable outcomes, but stability under a population adjustment dynamic need not imply that finite-sample learning agents can reach the same outcome through local reward feedback. We study this distinction in a transparent three-agent governance-motivated game involving a government, a platform firm, and users. We derive replicator dynamics for the fixed stage-game incentives, evaluate the cooperative evolutionary basin on a symmetric initial-condition grid, and compare it with learning-basin estimates for three decentralized value-based learners. The learning analysis uses independent Q-learning with $\varepsilon$-greedy action selection, scaled Boltzmann exploration, and SA--EA BQL under the same payoff environment and outcome criterion. The evolutionary basin has volume $V_E=1.00$ on the sampled grid. The empirical learning basin is $0.88$ for $\varepsilon$-IQL and $0.00$ for both scaled Boltzmann and SA--EA BQL. Diagnostic traces show that broader action diversity and nonzero value separation can coexist with failure to sustain the cooperative joint action in this fixed configuration. These results indicate that evolutionary stability and learning accessibility are distinct properties of a coupled game--learning system. The shared-bike setting is a motivating application; the broader contribution is a framework for comparing population-level stability with the finite-sample accessibility of cooperation under specified multi-agent learning dynamics.

A fundamental problem in noncooperative dynamic game theory is the computation of Nash equilibria under different information structures, which specify the information available to each agent during decision-making. Prior work has extensively studied equilibrium solutions for two canonical information structures: feedback, where agents observe the current state at each time, and open-loop, where agents only observe the initial state. However, these paradigms are often too restrictive to capture realistic settings exhibiting interleaved information structures, in which each agent observes only a subset of other agents at every timestep. To date, there is no systematic framework for modeling and solving dynamic games under arbitrary interleaved information structures. To this end, we make two main contributions. First, we introduce a method to model deterministic dynamic games with arbitrary interleaved information structures as Mathematical Program Networks (MPNs), where the network structure encodes the informational dependencies between agents. Second, for linear-quadratic (LQ) dynamic games, we leverage the MPN formulation to develop a systematic procedure for deriving Riccati-like equations that characterize Nash equilibria. Finally, we illustrate our approach through an example involving three agents exhibiting a cyclic information structure.