Value of information for a leader–follower partially observed Markov game
We consider a leader–follower partially observed Markov game (POMG) and analyze how the value of the leader’s criterion changes due to changes in the leader’s quality of observation of the follower. We give conditions that insure improved observation quality will improve the leader’s value function, assuming that changes in the observation quality do not cause the follower to change its policy. We show that discontinuities in the value of the leader’s criterion, as a function of observation quality, can occur when the change of observation quality is significant enough for the follower to change its policy. We present conditions that determine when a discontinuity may occur and conditions that guarantee a discontinuity will not degrade the leader’s performance. We show that when the leader and the follower are collaborative and the follower completely observes the leader’s initial state, discontinuities in the leader’s value function will not occur. However, examples show that improving observation quality does not necessarily improve the leader’s criterion value, whether or not the POMG is a collaborative game.