Screening in Vertical Oligopolies

A finite number of vertically differentiated firms simultaneously compete for and screen agents with private information about their payoffs. In equilibrium, higher firms serve higher types. Each firm distorts the allocation downward from the efficient level on types below a threshold, but upward above. While payoffs in this game are neither quasi-concave nor continuous, if firms are sufficiently differentiated, then any strategy profile that satisfies a simple set of necessary conditions is a pure-stategy equilibrium, and an equilibrium exists. A mixed-strategy equilibrium exists even when firms are less differentiated. The welfare effects of private information are drastically different than under monopoly. The equilibrium approaches the competitive limit quickly as entry costs grow small. We solve the problem of a multi-plant firm facing a type-dependent outside option and use this to study the effect of mergers.