Emergent Coordination through Game-Induced Nonlinear Opinion Dynamics

TL;DR

This paper introduces a game-theoretic approach using nonlinear opinion dynamics to enable autonomous agents to coordinate effectively despite initial indecision, with a novel synthesis method and stability analysis.

Contribution

It proposes a new procedure for synthesizing game-induced nonlinear opinion dynamics based on dynamic game value functions, including stability conditions and an optimization algorithm for agent policies.

Findings

Successfully coordinated agents in a simulated toll station scenario.

Provided stability conditions for game-induced opinion equilibria.

Demonstrated improved coordination in multi-agent decision-making.

Abstract

We present a multi-agent decision-making framework for the emergent coordination of autonomous agents whose intents are initially undecided. Dynamic non-cooperative games have been used to encode multi-agent interaction, but ambiguity arising from factors such as goal preference or the presence of multiple equilibria may lead to coordination issues, ranging from the "freezing robot" problem to unsafe behavior in safety-critical events. The recently developed nonlinear opinion dynamics (NOD) provide guarantees for breaking deadlocks. However, choosing the appropriate model parameters automatically in general multi-agent settings remains a challenge. In this paper, we first propose a novel and principled procedure for synthesizing NOD based on the value functions of dynamic games conditioned on agents' intents. In particular, we provide for the two-player two-option case precise stability conditions for equilibria of the game-induced NOD based on the mismatch between agents' opinions and their game values. We then propose an optimization-based trajectory optimization algorithm that computes agents' policies guided by the evolution of opinions. The efficacy of our method is illustrated with a simulated toll station coordination example.