Quasi-proportional mechanisms: Prior-free revenue maximization

Vahab Mirrokni, S. Muthukrishnan, Uri Nadav

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

    Abstract

    Inspired by Internet ad auction applications, we study the problem of allocating a single item via an auction when bidders place very different values on the item. We formulate this as the problem of prior-free auction and focus on designing a simple mechanism that always allocates the item. Rather than designing sophisticated pricing methods like prior literature, we design better allocation methods. In particular, we propose quasi-proportional allocation methods in which the probability that an item is allocated to a bidder depends (quasi-proportionally) on the bids. We prove that corresponding games for both all-pay and winners-pay quasi-proportional mechanisms admit pure Nash equilibria and this equilibrium is unique. We also give an algorithm to compute this equilibrium in polynomial time. Further, we show that the revenue of the auctioneer is promisingly high compared to the ultimate, i.e., the highest value of any of the bidders, and show bounds on the revenue of equilibria both analytically, as well as using experiments for specific quasi-proportional functions. This is the first known revenue analysis for these natural mechanisms (including the special case of proportional mechanism which is common in network resource allocation problems).

    Original languageEnglish (US)
    Title of host publicationLATIN 2010
    Subtitle of host publicationTheoretical Informatics - 9th Latin American Symposium, Proceedings
    Pages565-576
    Number of pages12
    DOIs
    StatePublished - 2010
    Event9th Latin American Theoretical Informatics Symposium, LATIN 2010 - Oaxaca, Mexico
    Duration: Apr 19 2010Apr 23 2010

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume6034 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference9th Latin American Theoretical Informatics Symposium, LATIN 2010
    CountryMexico
    CityOaxaca
    Period4/19/104/23/10

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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  • Cite this

    Mirrokni, V., Muthukrishnan, S., & Nadav, U. (2010). Quasi-proportional mechanisms: Prior-free revenue maximization. In LATIN 2010: Theoretical Informatics - 9th Latin American Symposium, Proceedings (pp. 565-576). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6034 LNCS). https://doi.org/10.1007/978-3-642-12200-2_49