Non-cooperative Tree Creation

Extended Abstract
  • Martin Hoefer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)


In this paper we consider the connection game, a simple network design game with independent selfish agents that was introduced by Anshelevich et al [4]. In addition we present a generalization called backbone game to model hierarchical network and backbone link creation between existing network structures. In contrast to the connection game each player considers a number of groups of terminals and wants to connect at least one terminal from each group into a network. In both games we focus on an important subclass of tree games, in which every feasible network is guaranteed to be connected.

For tree connection games, in which every player holds 2 terminals, we show that there is a Nash equilibrium as cheap as the optimum network. We give a polynomial time algorithm to find a cheap (2+ε)-approximate Nash equilibrium, which can be generalized to a cheap (3.1+ε)-approximate Nash equilibrium for the case of any number of terminals per player. This improves the guarantee of the only previous algorithm for the problem [4], which returns a (4.65+ε)-approximate Nash equilibrium. Tightness results for the analysis of all algorithms are derived.

For single source backbone games, in which each player wants to connect one group to a common source, there is a Nash equilibrium as cheap as the optimum network and a polynomial time algorithm to find a cheap (1+ε)-approximate Nash equilibrium.


Nash Equilibrium Polynomial Time Algorithm Steiner Tree Optimum Network Steiner Tree Problem 
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-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Hoefer
    • 1
  1. 1.Department of Computer & Information ScienceKonstanz UniversityKonstanzGermany

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