On the structure of two-person, finite, zero-sum games

Abstract

The algebraical and topological structure of the set S? resp. of all n x m matrix games with saddle points (resp. with unique saddle point) in the space R"*m of all such games is studied. It has been shown that S f is a closed cone with vertex zero and includes the origin. Moreover, it is neither convex nor dense subset of R" *m. The s e t i s a non-convex cone which does not include the origin. It is neither closed nor open. The concept of “reserve of non-saddlexity” has been also introduced.