On Type Deception in Linear-Quadratic Differential Games

2026-06-13

AI Summary

This study addresses the dynamic equilibrium of type deception and revelation in two-player linear-quadratic differential games under incomplete information. It innovatively formulates the interaction as an endogenous optimal revelation time problem, partitioning the game into a deceptive pooling phase followed by a full-information separating phase. The solution leverages nested Riccati equations integrated with optimal control theory, and introduces a gradient-based method for computing the optimal revelation time that maximizes the player’s value function. The framework is validated in a pursuit–evasion game, demonstrating the existence of an interior optimal revelation time and quantifying the ex ante gains from strategic deception. This work establishes a novel analytical framework for incomplete-information games in time-varying systems.

Abstract

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.

Problem

• type deception
• linear-quadratic differential games
• incomplete information
• signaling
• equilibrium

Innovation

• type deception
• linear-quadratic differential games
• incomplete information
• nested Riccati equations
• revelation time