Cooperative Stochastic Differential Games Research Articles

Existence of some optimal strategies in cooperative stochastic differential games

Cooperative games in which the dynamics are described by Ito equations are considered. Using a result of Elliott for zero-sum games we prove sufficient conditions for the existence of mean-square strategies and Nash-bargaining solutions in cooperative stochastic differential games.

Multi person decision analysis in large-scale hierarchical systems—team decision theory†

This paper represents a portion of a study of decision analysis in large-scale systems in which an effort is made to attack problem complexity by taking advantage of any inherent structure in the problem. By arranging the elements in the problem in an appropriate graphical form, usually a tree or hierarchy, it may often be possible to decompose the problem into a number of loosely coupled subproblems which can be solved independently and then coordinated in such a way as to provide a solution to the overall problem. We first survey team decision theory in which a multiplicity of decision makers, each of whom has access to different information, is attempting to extremize the same cost function. Under the conditions of a linear system with quadratic costs and Gaussian noises, the solution of a static team problem, in which no member's decision affects any other member's information, reduces to the solution of a set of linear algebraic equations. A large class of dynamic team problems which possess certain information structures is found to reduce to a static problem and hence can also be solved as a set of linear algebraic equations. Team problems can often be represented as cooperative stochastic differential games. Finally a technique is proposed for reducing the computational burden by decomposing the problem into a set of subproblems which can be solved relatively independently employing the techniques of hierarchical systems theory.