Dynamic Games for Adversarial and Cooperative Multi-Agents Control

Overview

Autonomous systems increasingly operate in environments where their behavior depends not only on physical dynamics and constraints, but also on the decisions of other autonomous or human agents. Examples include autonomous vehicles interacting on shared roads, robots transporting objects together, competitive robotic systems, and human–robot teams performing collaborative tasks. In these settings, treating other agents simply as equal or rational can lead to overly conservative or unrealistic behavior.

Our work develops dynamic-game-based control methods for multi-agent autonomous systems, with a particular focus on settings in which agents interact through shared physical and safety constraints. These interactions naturally lead to generalized Nash equilibrium (GNE) formulations, where the feasible decisions available to one player depend on the actions of the others.

A central theme of this research is that equilibrium selection matters. Standard formulations often impose a particular normalization of the shared-constraint multipliers, implicitly restricting how responsibility for satisfying a coupled constraint is distributed among the agents. We study non-normalized generalized Nash equilibria, where this distribution can be parameterized explicitly. This provides an additional mechanism for shaping multi-agent behavior—for example, assigning asymmetric responsibility in human–robot interaction or selecting more effective strategies in competitive robotic tasks.

We also investigate how dynamic-game solutions can be improved through learning across repeated interactions. For tasks that are executed repeatedly, previously successful joint trajectories can be used to construct terminal safe sets and cost-to-go approximations. This allows players to reuse experience while maintaining recursive feasibility and, under appropriate acceptance rules, avoiding degradation from one iteration to the next. The framework is particularly relevant to cooperative tasks in which several agents must agree on both a future joint state and an equilibrium strategy.