There are three main contributions of this thesis in equilibrium theory. The first is about the existence of equilibrium in discontinuous games. We find sufficient conditions for the existence of ε-Nash equilibrium in games with discontinuous payoff functions. In the second one, under time-varying discount factors we restate the Folk Theorems on the existence of equilibria of infinitely repeated games. The third one is about the existence of equilibrium in economies with indivisible goods. We re-formulate the model and the existence result of Danilov et al(2001) with more realistic cost functions, which depend on prices as well as the output level.