In this paper, we present ARF, our initial effort at solving taskallocation problems where cooperative agents need to perform tasks simultaneously. An example is multi-agent routing problems where several agents need to visit targets simultaneously, for example, to move obstacles out of the way cooperatively. First, we propose reaction functions as a novel way of characterizing the costs of agents in a distributed way. Second, we show how to approximate reaction functions so that their computation and communication times are polynomial. Third, we show how reaction functions can be used by a central planner to allocate tasks to agents. Finally, we show experimentally that the resulting task allocations are better than those of other greedy methods that do not use reaction functions. Categories and Subject Descriptors