Two-Criteria LQG Decision Problems with Decentralized Dynamic Information Patterns

Abstract

This paper discusses equilibrium solutions in multiperson two-criteria stochastic decision problems via a three-person two-criteria quadratic gaussian decision problem in which two of the decision makers (DM) have access to noisy static information and the third one has access to what the other two have observed as well as to noisy information on what they have done. For this class of problems, a set of sufficient conditions are given, under which there will exist a unique equilibrium solution. This equilibrium solution is shown to be linear in the observation of each DM and is related to the unique solution of a Liapunov-type matrix equation.If the third DM has also access to perfect information on what the other two DMs have done, then it is shown that the problem admits uncountably many equilibrium solutions.