Abstract
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.
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He, X., Kempe, D. (2013). Price of Anarchy for the N-Player Competitive Cascade Game with Submodular Activation Functions. In: Chen, Y., Immorlica, N. (eds) Web and Internet Economics. WINE 2013. Lecture Notes in Computer Science, vol 8289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45046-4_20
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DOI: https://doi.org/10.1007/978-3-642-45046-4_20
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