Within the current Internet, autonomous ISPs implement bilateral agreements, with each ISP establishing agreements that suit its own local objective to maximize its profit. Peering agreements based on local views and bilateral settlements, while expedient, encourage selfish routing strategies and discriminatory interconnections. From a more global perspective, such settlements reduce aggregate profits, limit the stability of routes, and discourage potentially useful peering/connectivity arrangements, thereby unnecessarily balkanizing the Internet. We show that if the distribution of profits is enforced at a global level, then there exist profit-sharing mechanisms derived from the coalition games concept of Shapley value and its extensions that will encourage these selfish ISPs who seek to maximize their own profits to converge to a Nash equilibrium. We show that these profit-sharing schemes exhibit several fairness properties that support the argument that this distribution of profits is desirable. In addition, at the Nash equilibrium point, the routing and connecting/peering strategies maximize aggregate network profits and encourage ISP connectivity so as to limit balkanization.