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Multilevel Network Games

  • Sebastian Abshoff
  • Andreas Cord-Landwehr
  • Daniel Jung
  • Alexander Skopalik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8877)

Abstract

We consider a multilevel network game, where nodes can improve their communication costs by connecting to a high-speed network. The n nodes are connected by a static network and each node can decide individually to become a gateway to the high-speed network. The goal of a node v is to minimize its private costs, i.e., the sum (SUM-game) or maximum (MAX-game) of communication distances from v to all other nodes plus a fixed price α > 0 if it decides to be a gateway. Between gateways the communication distance is 0, and gateways also improve other nodes’ distances by behaving as shortcuts. For the SUM-game, we show that for α ≤ n − 1, the price of anarchy is \(\Theta({n/\sqrt{\alpha}})\) and in this range equilibria always exist. In range α ∈ (n − 1,n(n − 1)) the price of anarchy is \(\Theta({\sqrt{\alpha}})\), and for α ≥ n(n − 1) it is constant. For the MAX-game, we show that the price of anarchy is either \(\Theta({1 + n/\sqrt{\alpha}})\), for α ≥ 1, or else 1. Given a graph with girth of at least 4α, equilibria always exist. Concerning the dynamics, both games are not potential games. For the SUM-game, we even show that it is not weakly acyclic.

Keywords

Nash Equilibrium Improve Response Communication Distance Private Cost 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.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sebastian Abshoff
    • 1
  • Andreas Cord-Landwehr
    • 1
  • Daniel Jung
    • 1
  • Alexander Skopalik
    • 1
  1. 1.Heinz Nixdorf Institute & Computer Science DepartmentUniversity of PaderbornPaderbornGermany

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