Heterogeneous Computing (HC) systems achieve high performance by networking together computing resources of diverse nature. The issues of task assignment and scheduling are critical in the design and performance of such systems. In this thesis, an auction based game theoretic framework is developed for dynamic task scheduling in HC systems. Based on the proposed game theoretic model, a new dynamic scheduling algorithm is developed that uses auction based strategies. The dynamic scheduling algorithm yields schedules with shorter completion times than static schedulers while incurring higher scheduling overhead. Thus, a second scheduling algorithm is proposed which uses an initial schedule generated with a learning automaton based algorithm, and then heuristics are used to identify windows of tasks within the application that can be rescheduled dynamically during run time.