We study dynamic task allocation when there is a fixed bipartite network associating workers to tasks. We analyze two approaches - centralized and decentralized. First, we study the optimal policy of a planner whose objective is to minimize the expected time of completion of all tasks. Second, we analyse a game played by workers who independently choose their tasks and are rewarded each time they complete a task. We show that both the planner’s and the worker’s problems are NP-hard and characterize networks for which the planner’s and workers’ policies are time-consistent. When policies are time-consistent the planner prefers the workers to start with the hardest tasks, whereas workers always prefer to start with easier tasks. We show that the two policies only coincide when the bipartite network satisfies a strong symmetry condition on the bipartite network. Differential rewards can be used to implement the planner’s optimal task allocation and we show that non-contingent rewards, which are independent of the set of remaining tasks, can be used as long as there is no task that a single agent can complete.