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Quality of Service in Network Creation Games

  • Andreas Cord-Landwehr
  • Alexander Mäcker
  • Friedhelm Meyer auf der Heide
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8877)

Abstract

Network creation games model the creation and usage costs of networks formed by n selfish nodes. Each node v can buy a set of edges, each for a fixed price α > 0. Its goal is to minimize its private costs, i.e., the sum (SUM-game, Fabrikant et al., PODC 2003) or maximum (MAX-game, Demaine et al., PODC 2007) of distances from v to all other nodes plus the prices of the bought edges. The above papers show the existence of Nash equilibria as well as upper and lower bounds for the prices of anarchy and stability. In several subsequent papers, these bounds were improved for a wide range of prices α. In this paper, we extend these models by incorporating quality-of-service aspects: Each edge cannot only be bought at a fixed quality (edge length one) for a fixed price α. Instead, we assume that quality levels (i.e., edge lengths) are varying in a fixed interval \([\check\beta,\hat\beta]\), \(0 < \check\beta \leq \hat\beta\). A node now cannot only choose which edge to buy, but can also choose its quality x, for the price p(x), for a given price function p. For both games and all price functions, we show that Nash equilibria exist and that the price of stability is either constant or depends only on the interval size of available edge lengths. Our main results are bounds for the price of anarchy. In case of the SUM-game, we show that they are tight if price functions decrease sufficiently fast.

Keywords

Nash Equilibrium Price Function Private Cost Selfish Node Distance Cost 
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.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Andreas Cord-Landwehr
    • 1
  • Alexander Mäcker
    • 1
  • Friedhelm Meyer auf der Heide
    • 1
  1. 1.Heinz Nixdorf Institute & Department of Computer ScienceUniversity of PaderbornGermany

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