Geodesic
Screening in space: rich and poor consumers in a linear city
Ural mathematical journal, Tome 7 (2021) no. 1, pp. 66-80

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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.
Keywords: screening, price discrimination, spatial competition, linear city, non-convex optimization.
Mots-clés : principal-Agent model 
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Sergey Kokovin; Fedor Vasilev. Screening in space: rich and poor consumers in a linear city. Ural mathematical journal, Tome 7 (2021) no. 1, pp. 66-80. http://geodesic.mathdoc.fr/item/UMJ_2021_7_1_a4/