Selfish Service Installation in Networks

(Extended Abstract)
  • Jean Cardinal
  • Martin Hoefer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)

Abstract

We consider a scenario of distributed service installation in privately owned networks. Our model is a non-cooperative vertex cover game for k players. Each player owns a set of edges in a graph G and strives to cover each edge by an incident vertex. Vertices have costs and must be purchased to be available for the cover. Vertex costs can be shared arbitrarily by players. Once a vertex is bought, it can be used by any player to fulfill the covering requirement of her incident edges. Despite its simplicity, the model exhibits a surprisingly rich set of properties. We present a cumulative set of results including tight characterizations for prices of anarchy and stability, NP-hardness of equilibrium existence, and polynomial time solvability for important subclasses of the game. In addition, we consider the task of finding approximate Nash equilibria purchasing an approximation to the optimum social cost, in which each player can improve her contribution by selfish defection only by at most a certain factor. A variation of the primal-dual algorithm for minimum weighted vertex cover yields a guarantee of 2, which is shown to be tight.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jean Cardinal
    • 1
  • Martin Hoefer
    • 2
  1. 1.Computer Science DepartmentUniversité Libre de Bruxelles, CP 212BrusselsBelgium
  2. 2.Department of Computer & Information ScienceKonstanz UniversityKonstanzGermany

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