Linear Quadratic Stochastic Differential Games under Asymmetric Value of Information

This paper considers a variant of two-player linear quadratic stochastic differential games. In this framework, none of the players has access to the state observations for all the time, which restricts the possibility of continuous feedback strategies. However, they can observe the state intermittently at discrete time instances by paying some finite cost. Having on demand costly measurements ensure that open-loop strategy is not the only strategy for this game. The individual cost functions for each player explicitly incorporate the value of information and the asymmetry that comes along with different costs of state observation for different players. We study the structural properties of the Nash equilibrium for this particular class of problems when the cost of observation is finite and positive. We show that the game problem simplifies into two decoupled game problems: one for deciding the control strategies, and the other for deciding the observation acquisition times. The study also reveals that under two extreme cases -cost of observation being 0 or∞the strategies coincide with feedback and open-loop strategies respectively.