A unified cooperative model for environmental costs in supply chains: the Shapley value for the linear case

This paper provides a normative framework based on cooperative game theory aimed at studying the problem of pollution responsibility allocation across multi-tier supply chains. The model is further developed with reference to the case of a linear supply chain, by using three responsibility principles (namely: Upstream, Downstream and Local Responsibility). Allocation rules are derived; also, desirable properties in terms of fairness, efficiency and transparency are introduced, in order to characterize such rules. Furthermore, a stability concept for efficient allocations is formulated. An example of a possible application of the introduced cost allocation rules is provided.