A key source of uncertainty in multi-agent systems is the behavior of other agents. Game-theoretic control approaches ignore this uncertainty, while robust control approaches treat others as fully adversarial. In this paper, we introduce strategically robust multi-agent control to populate the spectrum between these two paradigms. Specifically, in dynamic games, we propose that players are strategically robust and seek protection against misspecified control policies of the other players. This formulation induces a novel equilibrium concept, strategically robust dynamic equilibrium, that interpolates between game-theoretic control and robust control. We study this concept across canonical open- and closed-loop settings and show that accounting for strategic robustness also has computational benefits over classic approaches in game-theoretic control. Numerical experiments on vehicle platooning, inventory management, and network control illustrate resilience to misspecification, and also exhibit a "free-lunch" phenomenon in which strategic robustness can improve performance or social welfare.
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 (in the subgame-perfect sense) of such equilibria and 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.