Abstract
In a network creation game, initially proposed by Fabrikant et al. [11], selfish players build a network by buying links to each other. Each player pays a fixed price per link α> 0, and suffers an additional cost that is the sum of distances to all other players. We study an extension of this game where each player is only interested in its distances to a certain subset of players, called its friends. We study the social optima and Nash equilibria of our game, and prove upper and lower bounds for the “Price of Anarchy”, the ratio between the social cost of the worst Nash equilibria and the optimal social cost. Our upper bound on the Price of Anarchy is
where n is the number of players, α is the edge building price, and 
is the average number of friends per player. We derive a lower bound of Ω(logn / loglogn) on the Price of Anarchy.
Research partially supported by a grant of the Israel Science Foundation, BSF, and an IBM faculty award. A complete version of the paper can be found at .
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Halevi, Y., Mansour, Y. (2007). A Network Creation Game with Nonuniform Interests. In: Deng, X., Graham, F.C. (eds) Internet and Network Economics. WINE 2007. Lecture Notes in Computer Science, vol 4858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77105-0_28
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DOI: https://doi.org/10.1007/978-3-540-77105-0_28
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