We consider two-player linear-quadratic differential games of incomplete information, in which one player has a private type initially unknown to the other. The typed player has incentive to conceal their type, while the uninformed player has the potential to infer it during play. Any ex-ante equilibrium in this setting will decompose into a deceptive, pooling phase, and a complete-information, revelatory phase. We demonstrate how to solve both phases via nested Riccati equations. Candidate equilibria are then found by maximizing the game value over a scalar revelation time, for which we provide a gradient in the case of time-homogeneous system matrices. We conclude by demonstrating our framework in a pursuit-evasion game with time-varying control advantages, finding interior optimal revelation times that confirm deception has quantifiable ex-ante value.

翻译：本文研究不完全信息下的两人线性二次型微分博弈，其中一方拥有初始未知的私有类型。拥有类型的参与者有动机隐藏其类型，而未获知信息的一方则可能在博弈过程中推断该类型。在此设定下，任何事前均衡都将分解为欺骗性的汇集阶段与完全信息的揭示阶段。我们展示了如何通过嵌套的Riccati方程求解这两个阶段。候选均衡通过最大化标量揭示时间上的博弈价值得到，对于时间齐次系统矩阵的情况，我们给出了该价值的梯度。最后，我们通过具有时变控制优势的追逃博弈实例验证了该框架，发现了确认欺骗具有可量化事前价值的内点最优揭示时间。