In this paper the well-known minimax theorems of Wald, Ville and Von Neumann are generalized under weaker topological conditions onthe payoff function ƒ and/or extended to the larger set of the Borel probabilitymeasures instead of the set of mixed strategies.

In this paper the well-known minimax theorems of Wald, Ville and Von Neumann are generalized under weaker topological conditions onthe payoff function ƒ and/or extended to the larger set of the Borel probabilitymeasures instead of the set of mixed strategies.

In this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation scheme in...

In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming duality and the finite intersection property of compact sets. It turns out that these necessary and sufficient conditions have a clear interpretation within zero-sum...

In this paper we review and unify some of the classes of generalized convex functions introduced by different authors to prove minimax results in infinite dimensional spaces and show the relations between those classes. We also list for the most general class already introduced by Jeyakumar an...

In this note we review some known minimax theorems with applications in game theory and show that these results form an equivalent chain which includes the strong separation result in finite dimensional spaces between two disjoint closed convex sets of which one is compact. By simplifying the...

In this note we review some known minimax theorems with applications in game theory and show that these results form an equivalent chain which includes the strong separation result in finite dimensional spaces between two disjoint closed convex sets of which one is compact. By simplifying the...

In this chapter we give an overview on the theory of noncooperative games. In the first part we consider in detail for zero-sum (and constant-sum) noncooperative games under which necessary and sufficient conditions on the payoff function and different (extended) strategy sets for both players...

In this paper we discuss the level set method of Joó and how to use it to give an elementary proof of the well-known Sion’s minimax result. Although this proof technique is initiated by Joó and based on the inter-section of upper level sets and a clever use of the topological notion of...

In the first chapter of this book the basic results within convex and quasiconvex analysis are presented. In Section 2 we consider in detail the algebraic and topological properties of convex sets within Rn together with their primal and dual representations. In Section 3 we apply the results...