Strategically Robust Linear Quadratic Dynamic Games

TL;DR

This paper introduces a new framework for linear quadratic dynamic games where players are uncertain about each other's strategies, proposing a novel equilibrium concept and demonstrating its computational and practical advantages.

Contribution

It formalizes strategically robust dynamic games, establishes existence and uniqueness of equilibria, and shows they can be efficiently computed, with benefits demonstrated through simulations.

Findings

Existence and uniqueness of strategically robust equilibria.

Equilibrium policies are Markovian, linear, and computable via Riccati equations.

Robustness can improve social welfare without performance loss.

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.