Strategic Decision-Making in Multi-Agent Domains: A Weighted Constrained Potential Dynamic Game Approach

TL;DR

This paper introduces a novel approach using weighted constrained potential dynamic games to efficiently compute generalized Nash Equilibria in multi-agent decision-making, significantly reducing computational complexity and enabling practical applications.

Contribution

The paper proposes leveraging constrained dynamic potential games to transform complex multi-agent problems into single optimal control problems, improving solution efficiency.

Findings

Achieves significant solve time reduction compared to existing methods.

Successfully applies the approach to multi-robot navigation scenarios.

Demonstrates practical effectiveness through simulation and real-world experiments.

Abstract

In interactive multi-agent settings, decision-making and planning are challenging mainly due to the agents' interconnected objectives. Dynamic game theory offers a formal framework for analyzing such intricacies. Yet, solving constrained dynamic games and determining the interaction outcome in the form of generalized Nash Equilibria (GNE) pose computational challenges due to the need for solving constrained coupled optimal control problems. In this paper, we address this challenge by proposing to leverage the special structure of many real-world multi-agent interactions. More specifically, our key idea is to leverage constrained dynamic potential games, which are games for which GNE can be found by solving a single constrained optimal control problem associated with minimizing the potential function. We argue that constrained dynamic potential games can effectively facilitate interactive decision-making in many multi-agent interactions. We will identify structures in realistic multi-agent interactive scenarios that can be transformed into weighted constrained potential dynamic games (WCPDGs). We will show that the GNE of the resulting WCPDG can be obtained by solving a single constrained optimal control problem. We will demonstrate the effectiveness of the proposed method through various simulation studies and show that we achieve significant improvements in solve time compared to state-of-the-art game solvers. We further provide experimental validation of our proposed method in a navigation setup involving two quadrotors carrying a rigid object while avoiding collisions with two humans.