Optimal strategies for linear quadratic differential games with costly information

A two players stochastic differential game is considered with a given cost function. The players engage in a non-cooperative game where one tries to minimize the cost and the other tries to maximize the same. The players are given a dynamical system and their actions serve as the control inputs to the dynamical system. Their job is to control the state of this dynamical system to optimize the given objective function. We use the term “state of the game” to describe the state of this dynamical system. The challenge being that none of the players has access to the state of the game for all time, rather they can access the state intermittently and only after paying some information cost. Thus the cost structure is non-classical for a linear-quadratic game and it incorporates the value of information. We provide the Nash equilibrium strategy for the players under full state information access at no cost, as well as costly state information access. The optimal instances for accessing the state information are also provided for the players.