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 show that price of anarchy is constant already for α = O(n 1−ε ) for any fixed ε ≥ 1/ lg n, and show the general bound 2 O( √ lg n) on price of anarchy for all α.
The price of anarchy in network creation games
PODC '07
Mathematics Computer Science