Applications of α-strongly regular distributions to bayesian auctions

Richard Cole, Shravas Rao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Two classes of distributions that are widely used in the analysis of Bayesian auctions are the Monotone Hazard Rate (MHR) and Regular distributions. They can both be characterized in terms of the rate of change of the associated virtual value functions: for MHR distributions the condition is that for values v <vʹ, ø (vʹ) − ø (v) ≥ vʹ − v, and for regular distributions, ø (vʹ) − ø(v) ≥ 0. Cole and Roughgarden introduced the interpolating class of α-Strongly Regular distributions (α-SR distributions for short), for which ø (vʹ) − ø (v) ≥ α(vʹ− v), for 0 ≤ α ≤ 1. In this paper, we investigate five distinct auction settings for which good expected revenue bounds are known when the bidders’ valuations are given by MHR distributions. In every case, we show that these bounds degrade gracefully when extended to α-SR distributions. For four of these settings, the auction mechanism requires knowledge of these distribution(s) (in the other setting, the distributions are needed only to ensure good bounds on the expected revenue). In these cases we also investigate what happens when the distributions are known only approximately via samples, specifically how to modify the mechanisms so that they remain effective and how the expected revenue depends on the number of samples.

Original languageEnglish (US)
Title of host publicationWeb and Internet Economics - 11th International Conference, WINE 2015, Proceedings
PublisherSpringer Verlag
Pages244-257
Number of pages14
Volume9470
ISBN (Print)9783662489949
DOIs
StatePublished - 2015
Event11th International Conference on Web and Internet Economics, WINE 2015 - Amsterdam, Netherlands
Duration: Dec 9 2015Dec 12 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9470
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other11th International Conference on Web and Internet Economics, WINE 2015
CountryNetherlands
CityAmsterdam
Period12/9/1512/12/15

Fingerprint

Auctions
Hazards
Hazard Rate
Monotone
Rate of change
Valuation
Value Function
Distinct

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Cole, R., & Rao, S. (2015). Applications of α-strongly regular distributions to bayesian auctions. In Web and Internet Economics - 11th International Conference, WINE 2015, Proceedings (Vol. 9470, pp. 244-257). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9470). Springer Verlag. https://doi.org/10.1007/978-3-662-48995-6_18

Applications of α-strongly regular distributions to bayesian auctions. / Cole, Richard; Rao, Shravas.

Web and Internet Economics - 11th International Conference, WINE 2015, Proceedings. Vol. 9470 Springer Verlag, 2015. p. 244-257 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9470).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Cole, R & Rao, S 2015, Applications of α-strongly regular distributions to bayesian auctions. in Web and Internet Economics - 11th International Conference, WINE 2015, Proceedings. vol. 9470, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9470, Springer Verlag, pp. 244-257, 11th International Conference on Web and Internet Economics, WINE 2015, Amsterdam, Netherlands, 12/9/15. https://doi.org/10.1007/978-3-662-48995-6_18
Cole R, Rao S. Applications of α-strongly regular distributions to bayesian auctions. In Web and Internet Economics - 11th International Conference, WINE 2015, Proceedings. Vol. 9470. Springer Verlag. 2015. p. 244-257. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-48995-6_18
Cole, Richard ; Rao, Shravas. / Applications of α-strongly regular distributions to bayesian auctions. Web and Internet Economics - 11th International Conference, WINE 2015, Proceedings. Vol. 9470 Springer Verlag, 2015. pp. 244-257 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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