Infinite player noncooperative games with vector payoffs under relative pseudomonotonicity

In this paper we consider the Nash equilibrium problem for infinite player games with vector payoffs in a topological vector space setting. By employing new concepts of relative (pseudo) monotonicity, we establish several existence results of solutions for usual and normalized vector equilibria. The results strengthen existence results for vector equilibrium problems, which were based on classical pseudomontonicity concepts. They also extend previous results for vector variational inequalities and finite player games under relative (pseudo) monotonicity.