Abstract We study distributed task-allocation problems where cooperative agents need to perform some tasks simultaneously. Examples are multi-agent routing problems where several agents need to visit some targets simultaneously for example, to move obstacles out of the way cooperatively. In this paper, we ?rst generalize the concept o reaction functions proposed in the literature to charact ize the agent costs of performing multiple complex tasks Second, we show how agents can construct and approximate reaction functions in a distributed way. Third, we show how reaction functions can be used by an auctionlike algorithm to allocate tasks to agents. Finally, we show empirically that the team costs of our algorithms are substantially smaller than those of an existing stat of-the-art allocation algorithm for complex tasks.