Screening with Limited Information : The Minimax Theorem and A Geometric Approach

Research output: Chapters, Conference Papers, Creative and Literary Works (RGC: 12, 32, 41, 45)32_Refereed conference paper (with host publication)peer-review

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Author(s)

Detail(s)

Original languageEnglish
Title of host publicationWeb and Internet Economics
Subtitle of host publication17th International Conference, WINE 2021
EditorsMichal Feldman, Hu Fu, Inbal Talgam-Cohen
PublisherSpringer, Cham
Pages549
ISBN (Electronic)978-3-030-94676-0
ISBN (Print)978-3-030-94675-3
Publication statusPublished - Dec 2021

Publication series

NameLecture Notes in Computer Science
Volume13112
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Title17th International Conference on Web and Internet Economics (WINE 2021)
LocationVirtual
PlaceGermany
CityPotsdam
Period14 - 17 December 2021

Abstract

A seller seeks a selling mechanism to maximize the worst-case revenue obtained from a buyer whose valuation distribution lies in a certain ambiguity set. For a generic convex ambiguity set, we show via the minimax theorem that strong duality holds between the problem of finding the optimal robust mechanism and a minimax pricing problem where the adversary first chooses a worst-case distribution and then the seller decides the best posted price mechanism. This observation connects prior literature that separately studies the primal (robust mechanism design) and problems related to the dual (e.g., robust pricing, buyer-optimal pricing and personalized pricing). We provide a geometric approach to analytically solving the minimax pricing problem (and the robust pricing problem) for several important ambiguity sets such as the ones with mean and various dispersion measures, and with the Wasserstein metric. The solutions are then used to construct the optimal robust mechanism and to compare with the solutions to the robust pricing problem.

Research Area(s)

  • Robust mechanism design, Moment condition, Mean-preserving contraction, Wasserstein metric

Citation Format(s)

Screening with Limited Information: The Minimax Theorem and A Geometric Approach. / Chen, Zhi; Hu, Zhenyu; Wang, Ruiqin.
Web and Internet Economics: 17th International Conference, WINE 2021. ed. / Michal Feldman; Hu Fu; Inbal Talgam-Cohen. Springer, Cham, 2021. p. 549 (Lecture Notes in Computer Science; Vol. 13112).

Research output: Chapters, Conference Papers, Creative and Literary Works (RGC: 12, 32, 41, 45)32_Refereed conference paper (with host publication)peer-review