The automated assignment of multiple tasks to executing agents is a key problem in the area of multi-agent systems. In many domains, significant savings can be achieved by reallocating tasks among agents with different costs for handling tasks. The automation of task reallocation among self-interested agents requires that the individual agents use a common negotiation protocol that prescribes how they have to interact in order to come to an agreement on "who does what". In this paper, we introduce the multi-agent Traveling Salesman Problem(TSP) as an example of task reallocation problem, and suggest the Vickery auction as an interagent negotiation protocol for solving this problem. In general, auction-based protocols show several advantageous features: they are easily implementable, they enforce an efficient assignment process, and they guarantce an agreement even in scenarios in which the agents possess only very little domain-specific Knowledge. Furthermore Vickrey auctions have the additional advantage that each interested agent bids only once and that the dominant strategy is to bid one′s true valuation. In order to apply this market-based protocol into task reallocation among self-interested agents, we define the profit of each agent, the goal of negotiation, tasks to be traded out through auctions, the bidding strategy, and the sequence of auctions. Through several experiments with sample multi-agent TSPs, we show that the task allocation can improve monotonically at each step and then finally an optimal task allocation can be found with this protocol.