Equilibrium existence in games: Slight single deviation property and Ky Fan minimax inequality

In this paper, we exhibit a relation between the Nash equilibrium existence problem in ordinal games and the Ky Fan minimax inequality. In this way, we obtain new sufficient conditions for the existence of equilibria. The main tools used in the paper are a necessary condition introduced in [Nassah, R., Tian, G.: On the existence of Nash equilibrium in discontinuous games, Econ. Theory 61 (3), 515-540 (2016)] for normal form games and a generalization of the emph{single deviation property}. Examples compare our result with the previous ones