DUOPOLY MODELS WITH VERTICAL PRODUCT DIFFERENTIATION

This paper deals with duopoly models with vertical product differentiation. These are two-stage games. In the first stage, the quality game, the two firms choose their quality. In the second stage, the price game, they choose their prices. When the market is covered, the properties of this game are well known, even when the consumers are not uniformly distributed. When the market is uncovered the literature is not always clear about these models. In the present paper it is shown that the price game can be solved, when the consumers are distributed according to a distribution function with a log-concave density function.