Screening in space: Rich and poor consumers in a linear city
Unlike standard models of monopolistic screening (second-degree price discrimination), we consider a situation where consumers are heterogeneous not only vertically, in their willingness to pay, but also horizontally, in their tastes or "addresses'' a la Hotelling's Linear City. For such a screening game, a novel model is composed. We formulate the game as an optimization program, prove the existence of equilibria, develop a method to calculate equilibria, and characterize their properties. Namely, the solution structure of the resulting menu of contracts can be either a "chain of envy'' like in usual screening or a number of disconnected chains. Unlike usual screening, "almost all'' consumers get positive informational rent. Importantly, the model can be extended to oligopoly screening.