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International Conference on Algorithms and Complexity

CIAC 2015: Algorithms and Complexity pp 274–287Cite as

Sharing Non-anonymous Costs of Multiple Resources Optimally

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9079)

Abstract

In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources’ costs. We consider a general class of resource allocation problems in which a set of resources is used by a heterogeneous set of selfish users. The cost of a resource is a (non-decreasing) function of the set of its users. Under the assumption that the costs of the resources are shared by uniform cost sharing protocols, i.e., protocols that use only local information of the resource’s cost structure and its users to determine the cost shares, we exactly quantify the inefficiency of the resulting pure Nash equilibria. Specifically, we show tight bounds on prices of stability and anarchy for games with only submodular and only supermodular cost functions, respectively, and an asymptotically tight bound for games with arbitrary set-functions. While all our upper bounds are attained for the well-known Shapley cost sharing protocol, our lower bounds hold for arbitrary uniform cost sharing protocols and are even valid for games with anonymous costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users.

Keywords

  • Cost Function
  • Cost Sharing
  • Resource Allocation Problem
  • Congestion Game
  • Potential Game

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Most of the work was done while this author was at Technische Universität Berlin.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technische Universität Berlin, Berlin, Germany

    Max Klimm

  2. RWTH Aachen University, Aachen, Germany

    Daniel Schmand

Authors
  1. Max Klimm
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  2. Daniel Schmand
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Correspondence to Daniel Schmand .

Editor information

Editors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France

    Vangelis Th. Paschos

  2. Inst. of Theoretical Computer Science, ETH Zürich, Zürich, Switzerland

    Peter Widmayer

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Klimm, M., Schmand, D. (2015). Sharing Non-anonymous Costs of Multiple Resources Optimally. In: Paschos, V., Widmayer, P. (eds) Algorithms and Complexity. CIAC 2015. Lecture Notes in Computer Science(), vol 9079. Springer, Cham. https://doi.org/10.1007/978-3-319-18173-8_20

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  • DOI: https://doi.org/10.1007/978-3-319-18173-8_20

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