Multidimensional screening.
type: Item
instance of: scholarly article
title: Multidimensional screening.
zbMATH Open document ID: 1104.91023
author: Suren Basov
published in: Studies in Economic Theory
publication date: 2005-02-21T00:00:00Z
review text: This book is devoted to the mathematical background of multidimensional screening problem, that is the problem when the private information of the consumer cannot be capture in one characteristic. The general formulation of the problem of multidimensional screening is following. Assume a monopolist who faces a continuum of consumers produces a good of with \(n\) quality dimensions. The cost of production is given by function \(c(\cdot)\). Each consumer is interested in consuming at most one unit of the good and has a utility \(u(\alpha,x)-t\), where \(\alpha\in R^{m}\) is her unobservable type distributed on an open, bounded, convex set \(\Omega\subset R^{m}\) according to density function \(f(\cdot)\); \(t\) is the amount of money transferred to the monopolist. Consumers have an outside option of value \(s_0(\alpha)\). The monopolist announces a non-linear tariff \(t(\cdot)\). The amount \(t(x)\) determines how much a consumer has to pay for a good quality characteristics \(x\). So we have the following model. The monopolist selects a continuous \(t:\;R^{n}_{+}\to R\) to solve: \(\max\limits_{t(\cdot)}\int_{\Omega}(t(x(\alpha))-c(x(\alpha)))f(\alpha)\,d\alpha\), where \(c(x)\) is cost of producing a good with quality \(x\) and \(x(\alpha)\) satisfies \(x(\alpha)\in \text{ arg\,max} (u(\alpha,x)-t(x))\), \(\max(u(\alpha,x)-t(x))\geq s_0(\alpha)\). The book consists of two part. The first part gives a mathematical preliminaries. The Chapter~1 contains a review of vector calculus and introduces the basic operations and notions such as: the divergence, the gradient, conservative vector fields, curvilinear integrals, multiple and repeated integrals, flow of vector field, circulation of a vector field. The Chapter~2 contains the basic results and techniques of the theory of partial differential equations of the first and second order. The notions and properties of complete and general integrals, singular integral, method of characteristics are presented for the first ord…
reviewed by: Aleksandr D. Borisenko
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 91-01
Mathematics Subject Classification ID: 91B32
zbMATH DE Number: 2135751
zbMATH Keywords: multidimensional screening problem
zbMATH Keywords: monopolist
zbMATH Keywords: continuum of consumers
zbMATH Keywords: unidimensional screening model
zbMATH Keywords: the Spence-Mirrlees conditions
zbMATH Keywords: implementability
zbMATH Keywords: dual approach
zbMATH Keywords: Hamilton approach
zbMATH Keywords: type dependent participation constraint
zbMATH Keywords: random participation constraint
MaRDI profile type: Publication
full work available at URL: b138910
OpenAlex ID: W4238332870
DOI: 10.1007/B138910
description: scientific article; zbMATH DE number 2135751