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Internet and graphs are very much related. The graphical structure ofinternet has been studied extensively to provide efficient solutions to routingand other problems. But most of these studies assume a central authority whichcontrols and manages the internet. In the recent years game theoretic modelshave been proposed which do not require a central authority and the users areassumed to be routing their flows selfishly. The existence of Nash Equilibria,congestion and the amount of inefficiency caused by this selfish routing is amajor concern in this field. A type of paradox in the selfish routing networks,Braess' Paradox, first discovered by Braess, is a major contributor toinefficiency. Several pricing mechanisms have also been provided which give agame theoretical model between users(consumers) and ISPs ({Internet ServiceProviders} or sellers) for the internet.  We propose a novel pricing mechanism, based on real world Internet networkarchitecture, which reduces the severity of Braess' Paradox in selfish routinggame theoretic networks. It's a pricing mechanism between combinatorial usersand ISPs. We prove that Nash equilibria exists in this network and providebounds on inefficiency . We use graphical properties of internet to prove ourresult. Several interesting extensions and future work have also beendiscussed.

A real world network pricing game with less severe Braess' Paradox