Further Informational Properties of the Nash and Stackelberg Solutions of LQG Games

摘要

This paper considers a two-decision-maker problem where each decision maker has his own information and studies the impact of improving the information of only one decision maker. In a previous document an example of a two-decision-maker LQG static Nash game was considered and was shown for that particular example that, on the one hand, if one of the decision makers improves his own information by obtaining his opponent's information (while his opponent's information does not change) then he ends up with a higher Nash cost; on the other hand, if he improves his own information by getting an extra measurement not from his opponent (while his opponent's information does not change) then he might incur lower Nash cost. This paper proves that in a general two-decision-maker LQG static or dynamic Nash game, if one of the decision makers knows all his opponent's information, then more or better information for him alone is beneficial to him. In static games the authors prove that more information for one of the decision makes alone is beneficial to him provided that such information is orthogonal to both decision maker's information.