The Inefficiency of Equilibria in a Network Creation Game with Packet Forwarding

We study a novel variation of network creation games in which the players (vertices) form a graph by building undirected edges to each other with the goal of reducing their costs of using the network. The model we introduce assumes that a minimal set of nodes with high reachability from others are handed the responsibility of routing the traffic alongside the network, and thus these nodes would incur an extra cost for forwarding. We study Nash equilibrium in this model. We prove upper bounds on the price of anarchy, the worst-case ratio of social cost of Nash equilibria of the network to that of socially optimum solution, for different values of β. Specifically, we prove that the price of anarchy is O(n) for β = n, and also prove a tight upper bound of Θ(n) for β = n. Finally, we give some upper bounds when β takes a value between n and n.