In the framework of a vertical differentiation model where consumers are continuously distributed with respect to their intensity of preference for quality and their income, we studdy the optimal strategy of a natural monopoly : how many qualities to produce ? Which qualities should be produced...

In this paper, we present a more simple and independent proof of Reny's theorem (1998), on the existence of a Nash equilibrium in discontinue game, with a better-reply secure game in a Hausdorff topological vector space stronger than Reny's one. We will get the equivalence if the payoff function...