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Envy-Free Revenue Approximation for Asymmetric Buyers with Budgets

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Algorithmic Game Theory (SAGT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9928))

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Abstract

We study the computation of revenue-maximizing envy-free outcomes in a monopoly market with budgeted buyers. Departing from previous works, we focus on buyers with asymmetric combinatorial valuation functions over subsets of items. We first establish a hardness result showing that, even with two identical additive buyers, the problem is inapproximable. In an attempt to identify tractable families of the problem’s instances, we introduce the notion of budget compatible buyers, placing a restriction on the budget of each buyer in terms of his valuation function. Under this assumption, we establish approximation upper bounds for buyers with submodular valuations over preference subsets as well as for buyers with identical subadditive valuation functions. Finally, we also analyze an algorithm for arbitrary additive valuation functions, which yields a constant factor approximation for a constant number of buyers. We conclude with several intriguing open questions regarding budgeted buyers with asymmetric valuation functions.

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Author information

Authors and Affiliations

  1. Department of Informatics, Athens University of Economics and Business, Athens, Greece

    Evangelos Markakis

  2. Department of Digital Systems, University of Piraeus, Piraeus, Greece

    Orestis Telelis

Authors
  1. Evangelos Markakis
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  2. Orestis Telelis
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Correspondence to Orestis Telelis .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Martin Gairing

  2. University of Liverpool, Liverpool, United Kingdom

    Rahul Savani

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Markakis, E., Telelis, O. (2016). Envy-Free Revenue Approximation for Asymmetric Buyers with Budgets. In: Gairing, M., Savani, R. (eds) Algorithmic Game Theory. SAGT 2016. Lecture Notes in Computer Science(), vol 9928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53354-3_20

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  • DOI: https://doi.org/10.1007/978-3-662-53354-3_20

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