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Ordered contribution allocations: theoretical properties and applications

We introduce two general cost allocation methods that are based on the players’ ordered contributions to the total cost. The resulting allocations always are efficient in a game theoretic sense, and they are symmetric if the underlying order is symmetric with respect to the cost function. While the first of our methods is easily implementable for a large number of players, the second one always satisfies the dummy player property but, depending on the underlying order, can be computationally expensive. Our main application is a problem where the risk of an aggregate financial position has to be distributed among its constituent parts. In contrast with most existing methods our approach also works if the underlying risk measure has no particular properties such as coherency, convexity or differentiability. Therefore, it can for instance, be used in conjunction with Value-at-Risk, a widely used risk measure with none of the above properties. Moreover, it gives every player incentives to behave in a way that keeps the risk of the aggregate position low. As a second application we propose a nonlinear tax scheme for emissions of a pollutant such as CO2 that is able to enforce strict limits on total emissions.