The Existence Problem for Solutions

In 1944 John von Neumann and Oskar Morgenstern [18] presented an extensive development of a theory of n-person cooperative games in characteristic function form. The most basic and most challenging theoretical question regarding this theory concerns whether their solution sets exist. It has been known [5] since 1967 that such solutions need not exist in the most general case of all games. However, all known counterexamples are of a rather specialized nature, and there still remains large classes of games for which this question is unanswered. So this fundamental problem continues to be among the most important and intriguing problems in cooperative game theory, as well as one that appears most difficult to solve. The answer should prove of interest in both theory and applications.