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A group of firms has to divide the costs associated with environmental damages jointly generated as a by-product of their heterogeneous production activities. We propose a specific procedure to assign costs, the Linear Damage Equivalent Mechanism (LDE), which satisfies several appealing strategic and axiomatic properties. The LDE induces a strategic game that has an unambiguous noncooperative prediction, a unique Nash equilibrium which is also robust to coalitional deviations; moreover, the equilibrium is efficient. Among its other properties, we find that the LDE is immune to arbitrary changes in the units of account of the outputs.