Abstract:

This dissertation analyzes two models of Industrial Organization with multidimensional characteristics. The first model consists of a two-stage duopoly model of vertical product differentiation where each good is determined by N discrete characteristics. Consumers' tastes are described by an Elliptically Contoured Distribution. In the first stage both firms simultaneously choose what characteristics to include in their respective product. After observing the first stage product designs both firms compete in prices. It is proven that in any equilibrium one firm always includes all characteristics in the product. Moreover, when types have perfect positive correlation the unique equilibrium involves maximum differentiation. The main result states that the other firm's equilibrium level of differentiation is determined by the correlation between types. Conversely, for any given level of differentiation there exists a corresponding covariance matrix supporting it as an equilibrium outcome. No prediction with respect to the level of product differentiation can be made without knowledge of the correlation between types, and that, under certain assumptions, anything is possible with respect to product design in equilibrium.

The second model involves a monopolist selling multiple goods to a continuum of heterogeneous consumers. The implementation of Direct Revelation Mechanisms is analyzed in that setting, finding that it is possible for the monopolist to implement all Stochastic Incentive Compatible Mechanisms by committing to post a decreasing sequence of prices. The posted prices depend on time and have the desirable property of being step functions. When the optimal mechanisms are stochastic, it is optimal for the monopolist to price discriminate over time, contrary to the conventional wisdom that a single-good monopolist committed to an ex-ante price strategy will not price discriminate.

Both studies highlight the complexities and surprising results that can be obtained by extending traditional models to include multidimensionality.