On Network Formation Games with Heterogeneous Players and Basic Network Creation Games.

We consider two variants of the network formation game that aims to study the creation of large-scale networks and to capture the impact of selfish behavior, on behalf of the network administrators, on the overall network structure and performance. In particular, we study basic network creation games, where each player aims to minimize her distance to the remaining players, and we present an improved lower bound on the graph diameter of equilibria of this game. We also consider network formation games with a large number of heterogeneous players and monetary transfers, and prove tight bounds on the price of anarchy under realistic assumptions about the cost function. Finally, we argue about the setting where these heterogeneous players must be connected with additional edge-disjoint paths to mitigate the impact of failures.