Maximal element with applications to Nash equilibrium problems in Hadamard manifolds

ABSTRACT

The purpose of this paper is to study the existence of maximal elements with applications to Nash equilibrium problems for generalized games in Hadamard manifolds. By employing a KKM lemma, we establish a new maximal element theorem in Hadamard manifolds. As applications, some existence results of Nash equilibria for generalized games are derived. The results in this paper unify, improve and extend some known results from the literature.