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Network Bargaining: Using Approximate Blocking Sets to Stabilize Unstable Instances

  • Jochen Könemann
  • Kate Larson
  • David Steiner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7615)

Abstract

We study a network extension to the Nash bargaining game, as introduced by Kleinberg and Tardos [6], where the set of players corresponds to vertices in a graph G = (V,E) and each edge ij ∈ E represents a possible deal between players i and j. We reformulate the problem as a cooperative game and study the following question: Given a game with an empty core (i.e. an unstable game) is it possible, through minimal changes in the underlying network, to stabilize the game? We show that by removing edges in the network that belong to a blocking set we can find a stable solution in polynomial time. This motivates the problem of finding small blocking sets. While it has been previously shown that finding the smallest blocking set is NP-hard [2], we show that it is possible to efficiently find approximate blocking sets in sparse graphs.

Keywords

Extreme Point Cooperative Game Vertex Cover Bargaining Game Sparse Graph 
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 2012

Authors and Affiliations

  • Jochen Könemann
    • 1
  • Kate Larson
    • 2
  • David Steiner
    • 2
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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