In this paper we formulate and study a new scheduling problem called Selfish Multi-User Task Scheduling. This problem assumes that there are several users, each of them having multiple tasks that need processing on a set of parallel identical machines. Each user is selfish and her goal is to minimize the makespan of her own tasks. We model this problem as a non-cooperative, extensive-form game. We use the subgame perfect equilibrium solution concept to analyze the game which provides insight into the problem?s properties. We compute the price of anarchy to quantify the costs due to lack of coordination among the users.