The choice of the number of varieties : justifying simple mechanisms

Research output: Journal PublicationsJournal Article (refereed)

3 Citations (Scopus)

Abstract

We study a mechanism designerís trade-off between the complexity level and optimality level of a mechanism. While our techniques apply to a much larger class of mechanism design problems, we restrict our presentation to Mussa and Rosen (1978) quality di§erentiation in which a monopolist restricts itself to o§ering a menu with at most a Önite number n of varieties. We prove that (i) the marginal beneÖt of adding one more variety is diminishing in n; (ii) the loss due to the restriction on the number of varieties is of order no more than 1=n2 ; (iii) the marginal beneÖt of adding one more variety is of order no more than 1=n3 ; and (iv) o§ering only two varieties can make more than two-third of the potential proÖt that can be made by the second best o§ering. Roughly speaking, our analysis predicts that the monopolist should very plausibly o§er only a small number of varieties in the menu
Original languageEnglish
Pages (from-to)7-21
Number of pages15
JournalJournal of Mathematical Economics
Volume54
Early online date14 Aug 2014
DOIs
Publication statusPublished - Oct 2014
Externally publishedYes

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Mechanism Design
Diminishing
Optimality
Trade-offs
Restriction
Predict
Monopolist
Menu
Mechanism design
Presentation
Class

Keywords

  • Mechanism design
  • Nonlinear pricing
  • Short menu

Cite this

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title = "The choice of the number of varieties : justifying simple mechanisms",
abstract = "We study a mechanism designer{\'i}s trade-off between the complexity level and optimality level of a mechanism. While our techniques apply to a much larger class of mechanism design problems, we restrict our presentation to Mussa and Rosen (1978) quality di§erentiation in which a monopolist restricts itself to o§ering a menu with at most a {\"O}nite number n of varieties. We prove that (i) the marginal bene{\"O}t of adding one more variety is diminishing in n; (ii) the loss due to the restriction on the number of varieties is of order no more than 1=n2 ; (iii) the marginal bene{\"O}t of adding one more variety is of order no more than 1=n3 ; and (iv) o§ering only two varieties can make more than two-third of the potential pro{\"O}t that can be made by the second best o§ering. Roughly speaking, our analysis predicts that the monopolist should very plausibly o§er only a small number of varieties in the menu",
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The choice of the number of varieties : justifying simple mechanisms. / WONG, Adam Chi Leung.

In: Journal of Mathematical Economics, Vol. 54, 10.2014, p. 7-21.

Research output: Journal PublicationsJournal Article (refereed)

TY - JOUR

T1 - The choice of the number of varieties : justifying simple mechanisms

AU - WONG, Adam Chi Leung

PY - 2014/10

Y1 - 2014/10

N2 - We study a mechanism designerís trade-off between the complexity level and optimality level of a mechanism. While our techniques apply to a much larger class of mechanism design problems, we restrict our presentation to Mussa and Rosen (1978) quality di§erentiation in which a monopolist restricts itself to o§ering a menu with at most a Önite number n of varieties. We prove that (i) the marginal beneÖt of adding one more variety is diminishing in n; (ii) the loss due to the restriction on the number of varieties is of order no more than 1=n2 ; (iii) the marginal beneÖt of adding one more variety is of order no more than 1=n3 ; and (iv) o§ering only two varieties can make more than two-third of the potential proÖt that can be made by the second best o§ering. Roughly speaking, our analysis predicts that the monopolist should very plausibly o§er only a small number of varieties in the menu

AB - We study a mechanism designerís trade-off between the complexity level and optimality level of a mechanism. While our techniques apply to a much larger class of mechanism design problems, we restrict our presentation to Mussa and Rosen (1978) quality di§erentiation in which a monopolist restricts itself to o§ering a menu with at most a Önite number n of varieties. We prove that (i) the marginal beneÖt of adding one more variety is diminishing in n; (ii) the loss due to the restriction on the number of varieties is of order no more than 1=n2 ; (iii) the marginal beneÖt of adding one more variety is of order no more than 1=n3 ; and (iv) o§ering only two varieties can make more than two-third of the potential proÖt that can be made by the second best o§ering. Roughly speaking, our analysis predicts that the monopolist should very plausibly o§er only a small number of varieties in the menu

KW - Mechanism design

KW - Nonlinear pricing

KW - Short menu

UR - http://commons.ln.edu.hk/sw_master/4490

UR - http://www.scopus.com/inward/record.url?scp=84913526900&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2014.08.002

DO - 10.1016/j.jmateco.2014.08.002

M3 - Journal Article (refereed)

VL - 54

SP - 7

EP - 21

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

ER -