The Power of Two Prices: Beyond Cross-Monotonicity

  • Yvonne Bleischwitz
  • Burkhard Monien
  • Florian Schoppmann
  • Karsten Tiemann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)

Abstract

Assuming strict consumer sovereignty (CS*), when can cost-sharing mechanisms simultaneously be group-strategyproof (GSP) and β-budget-balanced (β-BB)? Moulin mechanisms are GSP and 1-BB for submodular costs. We overcome the submodularity requirement and instead consider arbitrary—yet symmetric—costs:

  • Already for 4 players, we show that symmetry of costs is not sufficient for the existence of a GSP and 1-BB mechanism. However, for only 3 players, we give a GSP and 1-BB mechanism.

  • We introduce two-price cost-sharing forms (2P-CSFs) that define players’ cost shares and present a novel mechanism that is GSP given any such 2P-CSF. For subadditive costs, we give an algorithm to compute 2P-CSFs that are \({\ensuremath{\frac{\sqrt{17} + 1}{4}}}\)-BB (≈ 1.28). This result is then shown to be tight for 2P-CSFs. Yet, this is a significant improvement over 2-BB, which is the best Moulin mechanisms can achieve.

  • We give applications to the minimum makespan scheduling problem.

A key feature of all our mechanisms is a preference order on the set of players. Higher cost shares are always payed by least preferred players.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yvonne Bleischwitz
    • 1
    • 2
  • Burkhard Monien
    • 1
  • Florian Schoppmann
    • 1
    • 2
  • Karsten Tiemann
    • 1
    • 2
  1. 1.Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, Fürstenallee 11, 33102 PaderbornGermany
  2. 2.International Graduate School of Dynamic Intelligent Systems 

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