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always exists with the price of stability in this game being at most the nth harmonic number in directed graphs. For undirected graphs, Anshelevich et al. presented a tight bound on the price of stability of 4/3 for a single source and two players case. Jian Li has proved that for undirected graphs with a distinguished destination to which all players must connect the price of stability of the Shapely network design game is where is the number of players. On the other hand, the price of anarchy

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