The basic concepts of three branches of game theory, leader-follower, cooperative, and two-person nonzero sum games, are reviewed and applied to the study of the Internet pricing issue. In particular, we emphasize that the cooperative game (also called the bargaining problem) provides an overall picture for the issue. With a simple model for Internet quality of service (QoS), we demonstrate that the leader-follower game may lead to a solution that is not Pareto optimal and in some cases may be "unfair," and that the cooperative game may provide a better solution for both the Internet service provider (ISP) and the user. The practical implication of the results is that government regulation or arbitration may be helpful. The QoS model is also applied to study the competition between two ISPs, and we find a Nash equilibrium point from which the two ISPs would not move out without cooperation. The proposed approaches can be applied to other Internet pricing problems such as the Paris Metro pricing scheme.