, Volume 72, Issue 1, pp 44–82 | Cite as

Enforcing Efficient Equilibria in Network Design Games via Subsidies

  • John Augustine
  • Ioannis CaragiannisEmail author
  • Angelo Fanelli
  • Christos Kalaitzis


The efficient design of networks has been an important engineering task that involves challenging combinatorial optimization problems. Typically, a network designer has to select among several alternatives which links to establish so that the resulting network satisfies a given set of connectivity requirements and the cost of establishing the network links is as low as possible. The Minimum Spanning Tree problem, which is well-understood, is a nice example.

In this paper, we consider the natural scenario in which the connectivity requirements are posed by selfish users who have agreed to share the cost of the network to be established according to a well-defined rule. The design proposed by the network designer should now be consistent not only with the connectivity requirements but also with the selfishness of the users. Essentially, the users are players in a so-called network design game and the network designer has to propose a design that is an equilibrium for this game. As it is usually the case when selfishness comes into play, such equilibria may be suboptimal. In this paper, we consider the following question: can the network designer enforce particular designs as equilibria or guarantee that efficient designs are consistent with users’ selfishness by appropriately subsidizing some of the network links? In an attempt to understand this question, we formulate corresponding optimization problems and present positive and negative results.


Network design Algorithmic game theory Equilibria Price of stability 



We thank Edith Elkind, Ning Chen, Nick Gravin, and Alex Skopalik for helpful discussions.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • John Augustine
    • 1
  • Ioannis Caragiannis
    • 2
    Email author
  • Angelo Fanelli
    • 3
  • Christos Kalaitzis
    • 4
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology MadrasChennaiIndia
  2. 2.Research Academic Computer Technology Institute & Department of Computer Engineering and InformaticsUniversity of PatrasRioGreece
  3. 3.CNRS and University of CaenCaenFrance
  4. 4.School of Computer and Communication SciencesÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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