Price of Anarchy for the N-Player Competitive Cascade Game with Submodular Activation Functions

  • Xinran He
  • David Kempe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8289)


We study the Price of Anarchy (PoA) of the competitive cascade game following the framework proposed by Goyal and Kearns in [11]. Our main insight is that a reduction to a Linear Threshold Model in a time-expanded graph establishes the submodularity of the social utility function. From this observation, we deduce that the game is a valid utility game, which in turn implies an upper bound of 2 on the (coarse) PoA. This cleaner understanding of the model yields a simpler proof of a much more general result than that established by Goyal and Kearns: for the N-player competitive cascade game, the (coarse) PoA is upper-bounded by 2 under any graph structure. We also show that this bound is tight.


Competitive cascade game Price of Anarchy Submodularity Valid utility game Influence maximization 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Xinran He
    • 1
  • David Kempe
    • 1
  1. 1.Computer Science DepartmentUniversity of Southern CaliforniaLos AngelesUSA

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