Online allocation and pricing with economies of scale

Avrim Blum, Yishay Mansour, Liu Yang*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Allocating multiple goods to customers in a way that maximizes some desired objective is a fundamental part of Algorithmic Mechanism Design. We consider here the problem of offline and online allocation of goods that have economies of scale, or decreasing marginal cost per item for the seller. In particular, we analyze the case where customers have unit-demand and arrive one at a time with valuations on items, sampled iid from some unknown underlying distribution over valuations. Our strategy operates by using an initial sample to learn enough about the distribution to determine how best to allocate to future customers, together with an analysis of structural properties of optimal solutions that allow for uniform convergence analysis. We show, for instance, if customers have {0, 1} valuations over items, and the goal of the allocator is to give each customer an item he or she values, we can efficiently produce such an allocation with cost at most a constant factor greater than the minimum over such allocations in hindsight, so long as the marginal costs do not decrease too rapidly. We also give a bicriteria approximation to social welfare for the case of more general valuation functions when the allocator is budget constrained.

Original languageEnglish
Title of host publicationWeb and Internet Economics - 11th International Conference, WINE 2015, Proceedings
EditorsGuido Schäfer, Evangelos Markakis
PublisherSpringer Verlag
Pages159-172
Number of pages14
ISBN (Print)9783662489949
DOIs
StatePublished - 2015
Event11th International Conference on Web and Internet Economics, WINE 2015 - Amsterdam, Netherlands
Duration: 9 Dec 201512 Dec 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9470
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th International Conference on Web and Internet Economics, WINE 2015
Country/TerritoryNetherlands
CityAmsterdam
Period9/12/1512/12/15

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