On Approximate Nash Equilibria in Network Design

  • Susanne Albers
  • Pascal Lenzner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6484)


We study a basic network design game where n self-interested agents, each having individual connectivity requirements, wish to build a network by purchasing links from a given set of edges. A fundamental cost sharing mechanism is Shapley cost sharing that splits the cost of an edge in a fair manner among the agents using the edge. In this paper we investigate if an optimal minimum-cost network represents an attractive, relatively stable state that agents might want to purchase. We resort to the concept of α-approximate Nash equilibria. We prove that for single source games in undirected graphs, any optimal network represents an H(n)-approximate Nash equilibrium, where H(n) is the n-th Harmonic number. We show that this bound is tight. We extend the results to cooperative games, where agents may form coalitions, and to weighted games. In both cases we give tight or nearly tight lower and upper bounds on the stability of optimal solutions. Finally we show that in general source-sink games and in directed graphs, minimum-cost networks do not represent good states.


Nash Equilibrium Directed Graph Network Design Undirected Graph Cooperative Game 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Susanne Albers
    • 1
  • Pascal Lenzner
    • 1
  1. 1.Department of Computer ScienceHumboldt-Universität zu BerlinBerlinGermany

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