Existence of doubly strong equilibria in generalized games and quasi-Ky Fan minimax inequalities

Using new sufficient conditions for the existence of solutions to quasi-Ky Fan minimax inequalities in infinite dimensional setting, we prove the existence of strategy profiles, called doubly strong equilibria, which maximize players' preferences in generalized games. Our setting allows discontinuous and non-ordered preferences. The doubly strong equilibrium is a refinement of the strong equilibrium by Aumann. We show that our conditions do not imply the previous ones that guarantee the existence of strong equilibria.