A method for constructing message systems for smooth performance functions

This paper examines the information content associated with any smooth, explicitly determined allocation function or performance function. The information content is characterized by the type of admitted privacy preserving message networks which implement the performance function (in the sense introduced by L. Hurwicz) and which belong to a specified class. A method is developed which provides the necessary and sufficient conditions which are satisfied by any admissible message network. This can be viewed as providing an alternative approach and extending the theory developed by L. Hurwicz, S. Reiter and D. Saari. Examples are provided to illustrate how these conditions can be used to obtain impossibility theorems and to construct message networks.