Linear quadratic Gaussian Stackelberg game under asymmetric information patterns

MARELLI, DAMIÁN; MENG, WEI; LI, ZHIPENG; CAI, QIANQIAN; FU, MINYUE

AUTOMATICA

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2021 vol. 125

0005-1098

This paper investigates the linear quadratic Gaussian Stackelberg game under asymmetric information. Two decision makers implement control strategies using different information patterns: The follower uses its observation information to design its strategy, whereas the leader implements its strategy using global information. For this problem, the separation principle becomes invalid. Instead, we apply the classical variation method to derive conditions to be satisfied by both decision makers. We show that the solution attributes to solving a two-point boundary value problem of stochastic version whose drift terms contain some conditional mean terms. We then propose a layered calculation method to solve this problem. In the inner layer calculation, the adjoint state variable´s estimate is expressed as a linear functional of the state estimate. In the outer layer calculation, the adjoint state variable is expressed as a linear functional of the state and its estimate. We also verify that the Kalman–Bucy filter works for computing the state estimate. The result is also applied to dynamic duopoly with sticky prices and pursuit–evasion problem.