Probabilistic Observation Strategies in Stochastic Differential Games with Costly Measurements

When obtaining measurements of a system state is costly, it is important to determine when the benefits of having a measurement will out weigh its cost. Here discrete LQG sequential differential games are considered, and the optimal observation strategies are seen to depend in a fundamental way on the game information structure. Three structures are treated, and the observation decision at each stage in the game is allowed to be probabilistic rather than deterministic in order to allow the players to optimize in an ensemble average sense over many games.