In this dissertation, the central objective is to achieve fairness in bandwidth sharing amongst selfish users in a distributed system. Because of the inherent contention-based nature of the distributed medium access and the selfishness of the users, the distributed medium access is modeled as a non-cooperative game; designated as the Access Game. A p-CSMA type medium access scenario is proposed for all the users. Therefore, in the Access Game, each user has two actions to choose from: transmit and wait . The outcome of the Access Game and payoffs to each user depends on the actions taken by all the users. Further, the utility function of each user is constructed as a function of both Quality of Service (QoS) and Battery Power (BP). Various scenarios involving the relative importance of QoS and BP are considered. It is observed that, in general the Nash Equilibrium of the Access Game does not result into fairness. Therefore, Constrained Nash Equilibrium is proposed as a solution. The advantage of Constrained Nash Equilibrium is that it can be predicated on the fairness conditions and the solution will be guaranteed to result in fair sharing of bandwidth. However, Constrained Nash Equilibrium is that it is not self-enforcing. Therefore, two mechanisms are proposed to design the Access Game in such a way that in each case the Nash Equilibrium of the Access Game satisfies fairness and maximizes throughput. Hence, with any of these mechanisms the solution of the Access Game becomes self-enforcing