Strategically Robust Linear Quadratic Dynamic Games

2026-04-24

AI Summary

This study addresses strategic vulnerability in linear-quadratic dynamic games arising from players’ uncertainty about each other’s strategies or objectives by introducing the notion of strategic robustness. The authors formulate a fictitious game framework in which each player faces an adversarial counterpart penalized for deviating from its nominal belief-based strategy. Within this setting, they propose a novel solution concept—strategic robust dynamic equilibrium—and establish its existence, uniqueness, and Markovian linear structure. Remarkably, they uncover a “free lunch” phenomenon wherein robustness simultaneously enhances individual utility and social welfare. By solving a system of coupled backward Riccati equations and integrating tools from robust control and risk-sensitive game theory, the work yields computationally efficient, decentralized strategies. Numerical simulations confirm that the proposed approach achieves performance gains without sacrificing computational tractability.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Adversarial Learning & Robustness
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We study linear quadratic dynamic games where players are uncertain about each other's control policies or goals and consequently seek to be strategically robust. Building on recent work on strategically robust and risk-averse game theory, we first formalize the problem of strategically robust linear quadratic dynamic games. We show that these can be rewritten as simple transformations of linear quadratic games in which each player chooses a controller in a fictitious game in which they are faced with an adversary who is penalized for deviating from the other players' policies. This formulation naturally induces a novel notion of dynamic equilibrium, which we call a strategically robust dynamic equilibrium. We establish existence and uniqueness of such equilibria and furthermore show that the equilibrium policies are Markovian, linear, and can be efficiently computed via coupled backward Riccati equations. Through numerical simulations, including experiments in a network game, we illustrate the benefits of strategic robustness in designing robust and resilient decentralized control schemes. Our experiments also expose a "free-lunch" phenomenon in games in which robustness does not incur a corresponding loss in performance but can yield improvements in players' utilities and social welfare.

Problem

• strategic robustness
• linear quadratic dynamic games
• uncertainty
• dynamic equilibrium
• decentralized control

Innovation

• strategically robust equilibrium
• linear quadratic dynamic games
• coupled Riccati equations
• risk-averse game theory
• decentralized control