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Envy-Free Pricing in Multi-item Markets

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Automata, Languages and Programming (ICALP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6199))

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Abstract

In this paper, we study the revenue maximization envy-free pricing in multi-item markets: there are m items and n potential buyers where each buyer is interested in acquiring one item. The goal is to determine allocations (a matching between buyers and items) and prices of all items to maximize the total revenue given that all buyers are envy-free.

We give a polynomial time algorithm to compute a revenue maximization envy-free pricing when every buyer evaluates at most two items a positive valuation, by reducing it to an instance of weighted independent set in a perfect graph and applying the Strong Perfect Graph Theorem. We complement our result by showing that the problem becomes NP-hard if some buyers are interested in at least three items.

Next we extend the model to allow buyers to demand a subset of consecutive items, motivated from TV advertising where advertisers are interested in different consecutive slots with different valuations and lengths. We show that the revenue maximization envy-free pricing in this setting can be computed in polynomial time.

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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

    Ning Chen

  2. Department of Computer Science, City University of Hong Kong, Hong Kong

    Xiaotie Deng

Authors
  1. Ning Chen
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  2. Xiaotie Deng
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Editor information

Editors and Affiliations

  1. Computing Laboratory, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Samson Abramsky

  2. Université de Bordeaux (LaBRI) & INRIA, 351, cours de la Libération, 33405, Talence Cedex, France,

    Cyril Gavoille

  3. INRIA, Centre de Recherche Bordeaux – Sud-Ouest, 351 cours de la Libération, 33405, Talence Cedex, France

    Claude Kirchner

  4. Heinz Nixdorf Institute, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Friedhelm Meyer auf der Heide

  5. University of Patras and RACTI, 26500, Patras, Greece

    Paul G. Spirakis

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Chen, N., Deng, X. (2010). Envy-Free Pricing in Multi-item Markets. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14162-1_35

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  • DOI: https://doi.org/10.1007/978-3-642-14162-1_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14161-4

  • Online ISBN: 978-3-642-14162-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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