Reassessing global carbon footprints of co-produced metals using Shapley values: a portfolio-based allocation approach

Abstract Allocation in multi-product systems is one of the controversial problems of life cycle assessment (LCA). It is currently only solved using heuristic approaches in particular as applied to the mining of minerals containing several valuable metals. Economic allocation is operationally straightforward but can yield strongly time-dependent allocation results when relative metal prices fluctuate. The proposed Shapley approach from game theory removes this specific source of variability because prices are not model inputs. It does not derive mine-specific allocation factors. Its objective is to estimate portfolio-average mine-site GHG emission intensities for gold, silver, copper, lead and zinc from a global 2021 portfolio of 726 mines. It is not the mines and mining companies that are regarded as actors, but rather the metals, which are treated as players in a game. The term ‘player’ is used solely in its mathematical sense and does not imply agency, cooperation, negotiation or economic behaviour. Coalition values are constructed from the observed annual mine portfolio, and a Shapley value averages incremental contributions over structurally admissible metal orders. Using real data sets from the mining industry, GHG emission factors for the metals Au, Ag, Cu, Pb and Zn are calculated for the year 2021. The emission factor for Au is therefore ≈ 16,900 kg CO 2 e per kg Au, for Ag ≈ 2400 kg CO 2 e/kg and for Cu ≈ 2.8 kg CO 2 e/kg after adding generic downstream contributions for comparison. The approach is price-independent and conserves the observed portfolio total, but its results are conditional on the portfolio boundary, the admissible-coalition rule and the proprietary data coverage. It is an attributional accounting method. This shows that game theory concepts should be given greater consideration in allocation issues in LCA.