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This paper addresses task allocation to coordinate a fleet of autonomous vehicles by presenting two decentralized algorithms: the consensus-based auction algorithm (CBAA) and its generalization to the multi-assignment problem, i.e., the consensus-based bundle algorithm (CBBA). These algorithms utilize a market-based decision strategy as the mechanism for decentralized task selection and use a consensus routine based on local communication as the conflict resolution mechanism to achieve agreement on the winning bid values. Under reasonable assumptions on the scoring scheme, both of the proposed algorithms are proven to guarantee convergence to a conflict-free assignment, and it is shown that the converged solutions exhibit provable worst-case performance. It is also demonstrated that CBAA and CBBA produce conflict-free feasible solutions that are robust to both inconsistencies in the situational awareness across the fleet and variations in the communication network topology. Numerical experiments confirm superior convergence properties and performance when compared with existing auction-based task-allocation algorithms.