An equilibrium theory for multi-person decision making with multiple probabilistic models: Part II: Asymmetric mode of decision making

This paper develops an equilibrium theory for two-person two-criteria stochastic decision problems with static information patterns and an asymmetric mode of decision making, wherein the decision makers have different probabilistic models of the underlying process. The objective functions are quadratic and the decision spaces are general inner-product spaces. Firstly, a set of sufficient conditions is obtained for existence and uniqueness of Stackelberg equilibria, and a uniformly convergent iterative scheme is developed, whereby the equilibrium policy of the leader can be obtained by evaluating a number of conditional expectations. When the probability measures are Gaussian, the equilibrium solution is shown to be generically non-linear, with the linear structure prevailing only in some special cases which are delineated in the paper.