A Forward-Inverse Dynamic Game Framework for Enhanced Multi-Agent Trajectory Planning

DynoJEPP is a factor-graph-based framework that jointly formulates and simultaneously optimizes estimation, prediction, and planning in dynamic environments. In conventional factor-graph-based approaches that jointly formulate estimation, prediction, and planning, information from prediction and planning feeds back into state estimation, yielding corrupted estimates, undesired behaviors, and unsafe plans. To address this, DynoJEPP introduces a novel directed factor that enforces directional information flow within the factor graph, preventing prediction and planning from corrupting state estimation. We evaluate the impact of directed factors on inter-module interactions during navigation in both static and dynamic environments. Our results demonstrate that these factors are critical for safe operation, as without them, the robot collides in the majority of experiments. Building on this, we further introduce Cooperative DynoJEPP, which enables the ego robot to incorporate cooperative object behavior into its prediction and trajectory planning.

We propose a game-theoretic framework for adaptive multi-agent intelligent systems. Unlike classical game theory, which often treats strategies as primitive objects chosen by perfectly rational agents, the proposed framework provides a mathematical foundation for studying equilibrium in NeuroAI and can be viewed as an extension of game theory under relaxed assumptions, including partial observability, bounded computation, and uncertainty. At its core, Multilevel Interactive Equilibrium (MIE) generalizes the classical Nash equilibrium to intelligent systems with internal computation. Rather than being defined solely at the level of observable behavior, equilibrium emerges when neural learning dynamics, cognitive representations, and behavioral strategies mutually stabilize between interacting agents. This framework applies uniformly to interactions between two biological brains, two artificial agents, or hybrid human-AI systems. We discuss applications of multilevel game theory to human-autonomous vehicle driving, human-machine interaction, human-large language model (LLM) interaction, and computational psychiatry. We also outline experimental strategies and computational methods for estimating MIE and discuss challenges and prospects for future research.

Mean field games efficiently approximate a very large population of strategic agents. While these games can aid the understanding of complex systems, their deployment in real-world settings is challenged by the specification of their parameters: mean field games (MFGs) often involve hidden preferences, constraints, and interactions that can rarely be theoretically derived or directly observed. To address this gap, we present a neural network-based framework for learning parametric, finite-state MFGs from observed population dynamics. To do so, we formulate the parameter calibration as an inverse problem and use implicit differentiation to backpropagate through the games' equilibrium. The resulting approach is fully differentiable and enables us to estimate flexible trajectory-wise parameter paths, including state- and time-dependent specifications without requiring observations of the individual agents' actions or rewards. We provide a proof for the exactness of the gradient computation in a discrete-time formulation. We validate our framework through numerical experiments across four systems of increasing complexity, ranging from synthetic linear-quadratic benchmarks to real-world urban mobility datasets.