Stability and Sensitivity Analysis for Objective Misspecifications Among Model Predictive Game Controllers

TL;DR

This paper investigates how inaccuracies in game models affect the stability and equilibrium sensitivity of multi-agent systems using model predictive game controllers.

Contribution

It provides stability criteria and sensitivity analysis for multi-agent systems with heterogeneous predictive game controllers under model misspecifications.

Findings

Established stability conditions for multi-agent systems with model misspecifications.

Quantified how equilibrium outcomes change with variations in agents' game parameters.

Analyzed the impact of model inaccuracies on collective behavior in multi-agent control.

Abstract

Model-based multi-agent control requires agents to possess a model of the behavior of others to make strategic decisions. Solution concepts from game theory are often used to model the emergent collective behavior of self-interested agents and have found active use in multi-agent control design. Model predictive games are a class of controllers in which an agent iteratively solves a finite-horizon game to predict the behavior of a multi-agent system and synthesize their own control action. When multiple agents implement these types of controllers, there may exist misspecifications in the respective game models embedded in their controllers, stemming from inaccurate estimates or conjectures of other agents' objectives. This paper analyzes the resulting prediction misalignments and their effects on the system's behavior. We provide criteria for the stability of multi-agent dynamic systems with heterogeneous model predictive game controllers, and quantify the sensitivity of the equilibria to individual agents' game parameters.