Computer network bandwidth can be viewed as a limited resource. The users on the network compete for that resource. Their competition can be simulated using game theory models. No centralized regulation of network usage is possible because of the diverse ownership of network resources. Therefore, the problem is of ensuring the fair sharing of network resources. If a centralized system could be developed which would govern the use of the shared resources, each user would get an assigned network usage time or bandwidth, thereby limiting each person's usage of network resources to his or her fair share. As of yet, however, such a system remains an impossibility, making the situation of sharing network resources a competitive game between the users of the network and decreasing everyone's utility. This chapter explores this competitive game.