We study Nash equilibria in the setting of network creation games introduced recently by Fabrikant, Luthra, Maneva, Papadimitriou and Shenker. In this game we have a set of selfish node players, each creating some incident links, and the goal is to minimize α times the cost of the created links plus sum of the distances to all other players. Fabrikant et al. proved an upper bound O( √ α) on the price of anarchy, i.e., the relative cost of the lack of coordination. Albers, Eilts, Even-Dar, Mansour, and Roditty show that the price of anarchy is constant for α = O( √ n) and for α ≥ 12 n lg n , and that the price of anarchy is 15
Demaine et al. REF introduced MAXGAME as a natural variant of network creation games, and showed that price of anarchy of MAXGAME is at most 2 for α ≥ n, O(min{4
The price of anarchy in network creation games
PODC '07
Mathematics Computer Science