Linear Quadratic Games with Costly Measurements
Date: December 12 - December 15, 2017
In this work we consider a stochastic linear quadratic two-player game.The state measurements are observed through a switched noiseless communication link. Each player incurs a ﬁnite cost every time the link is established to get measurements. Along with the usual control action, each player is equipped with a switching action to control the communication link. The measurements help to improve the estimate and hence reduce the quadratic cost, but at the same time the cost is increased due to switching. We study the subgame perfect equilibrium control and switching strategies for the players. We show that the problem can be solved in a two-step process by solving two dynamic programming problems. The ﬁrst step corresponds to solving a dynamic programming for the control strategy and the second step involves solving another dynamic programming for the switching strategy.