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.

翻译：我们研究线性二次动态对策，其中博弈方对彼此的控制策略或目标存在不确定性，因此寻求策略上的稳健性。基于近期关于策略稳健与风险厌恶博弈论的工作，我们首先形式化定义了策略稳健线性二次动态对策问题。我们证明，这些问题可简化为线性二次对策的简单变换形式：在虚拟博弈中，每个博弈方选择一个控制器，并面对一个因偏离其他博弈方策略而受到惩罚的对手。该形式自然引出了动态均衡的新概念，我们称之为策略稳健动态均衡。我们证明了此类均衡的存在性与唯一性，并进一步表明均衡策略具有马尔可夫性、线性特性，且可通过耦合的逆推Riccati方程高效计算。通过数值仿真（包括网络博弈实验），我们展示了策略稳健性在设计稳健且具有弹性的分散式控制方案中的优势。实验还揭示了博弈中的"免费午餐"现象：稳健性不仅不会导致性能损失，反而能提升博弈方的效用与社会福利。