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We propose a decentralized game-theoretic framework for dynamic task allocation problems for multi-agent systems. In our problem formulation, the agents' utilities depend on both the rewards and the costs associated with the successful completion of the tasks assigned to them. The rewards reflect how likely is for the agents to accomplish their assigned tasks whereas the costs reflect the effort needed to complete these tasks (this effort is determined by the solution of corresponding optimal control problems). The task allocation problem considered herein corresponds to a dynamic game whose solution depends on the states of the agents in contrast with classic static (or single-act) game formulations. We propose a greedy solution approach in which the agents negotiate with each other to find a mutually agreeable (or individually rational) task assignment profile based on evaluations of the task utilities that reflect their current states. We illustrate the main ideas of this work by means of extensive numerical simulations.