An Equilibrium Theory for Multiperson Decision Making with Multiple Probabilistic Models

This paper develops an equilibrium theory for two-person two-criteria stochastic decision problems with static information patterns, wherein the decision makers (DM“s) have different probabilistic models of the underlying process, the objective functionals are quadratic, and the decision spaces are general inner-product spaces. Under two different modes of decision making (viz. symmetric and asymmetric), sufficient conditions are obtained for the existence and uniqueness of equilibrium solutions (stable in the former case), and in each case a uniformly convergent iterative scheme is developed whereby the equilibrium policies of the DM's can be obtained by evaluating a number of conditional expectations. When the probability measures are Gaussian, the equilibrium solution is linear under the symmetric mode of decision making, whereas it is generically nonlinear in the asymmetric case, with the linear structure prevailing only in some special cases which are delineated in the paper.