Stochastic Differential Linear-Quadratic Games with Intermittent Asymmetric Observations

In this paper, we consider a two-players stochastic linear quadratic game framework. The game is partially observed and each player has their own private observation. The challenge is that none of the players has access to the continuum observations, rather they can access their respective observations at discrete time instances by operating a switch unanimously. The operation of the switch is costly and hence the gathering of the observations are costly. Each player is equipped with finite memory and she can only use the latest observation to construct the control strategy. The private observations of the players lead to a source of asymmetry in this game. Moreover, the players have different costs for operating the switch, which is another source of asymmetry. We study the structural properties of the Nash equilibrium for this particular class of problems and then we finally show that the switching problem simplifies to a bi-objective optimization problem.