On Type Deception in Linear-Quadratic Differential Games
Provides a tractable framework for analyzing strategic deception in dynamic games, relevant to game theory and control theory communities.
The paper models deception in linear-quadratic differential games where one player has a private type. It shows that optimal play involves a deceptive pooling phase followed by revelation, and solves both phases using nested Riccati equations, demonstrating quantifiable value of deception in a pursuit-evasion example.
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.