SCREENING IN SPACE: RICH AND POOR CONSUMERS IN A LINEAR CITY

• Main Authors: Sergey Kokovin, Fedor Vasilev
• Format: Article
• Language: English
• Published: Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. 2021-07-01
• Series: Ural Mathematical Journal
• Subjects: screening, price discrimination, spatial competition, linear city, principal-agent model, non-convex optimization
• Online Access: https://umjuran.ru/index.php/umj/article/view/376

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.