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Social Welfare in One-Sided Matching Markets without Money

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2011, RANDOM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6845))

Abstract

We study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent’s utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation.

We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526,2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first non-trivial performance guarantees for these natural mechanisms.

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Authors and Affiliations

  1. Department of Computer and Information Science, University of Pennsylvania, USA

    Anand Bhalgat, Deeparnab Chakrabarty & Sanjeev Khanna

Authors
  1. Anand Bhalgat
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  2. Deeparnab Chakrabarty
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  3. Sanjeev Khanna
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Liverpool, Ashton Building, L69 3BX, Liverpool, UK

    Leslie Ann Goldberg

  2. Department of Computer Science, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, 15213, Pittsburgh, PA, USA

    R. Ravi

  4. Centre Universitaire d’Informatique,, University of Geneva,, Battelle A 7 route de Drize, 1227, Carouge, Switzerland

    José D. P. Rolim

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© 2011 Springer-Verlag Berlin Heidelberg

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Bhalgat, A., Chakrabarty, D., Khanna, S. (2011). Social Welfare in One-Sided Matching Markets without Money. In: Goldberg, L.A., Jansen, K., Ravi, R., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2011 2011. Lecture Notes in Computer Science, vol 6845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22935-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-22935-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22934-3

  • Online ISBN: 978-3-642-22935-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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