A discussion of the consistency axiom in cost-allocation problems

The recent literature on cost allocation lacks consensus on what is an appropriate definition of the consistency axiom. We take this as evidence that a careful reexamination is necessary. The starting point of our critique is the widely adopted definition proposed in Moulin and Shenker (1994), which we show to be conceptually flawed. Rectifying this flaw leads to a definition of consistency which already appeared in the recent literature though without satisfactory conceptual justification. We offer a classification of the existing definitions of the consistency axiom by relating them to the definitions of consistency in cooperative games suggested in Davis and Maschler (1965) and Hart and Mas-Colell (1989). We argue that only the latter leads to a meaningful interpretation of consistency when production externalities are present.

- A PROCEDURE FOR SHARING RECYCLING COSTS

This paper examines a situation in which the production activities of different agents, in a common geographical location, create waste products that are either of a similar biological or chemical composition or offer commercially compatible combinations. What we propose here, therefore, is a cost-sharing model for the of recycling of their waste products. We concentrate, however, on the specific case in which the agents' activities are heterogeneous. We first examine, from a normative point of view, the cost-sharing rule, which we shall call the multi-commodity serial (MCS) rule. We introduce a property, that we call Cost-Based Equal Treatment, and we demonstrate that the unique rule verifying the Serial Principle and this property is the MCS rule. We then deal with the analysis of the agents' strategic behavior when they are allowed to select their own production levels, in which case the total cost is then split, in accordance with the MCS rule. We show that there is only one Nash equilibrium, which is obtained from an interactive elimination of dominated strategies.Cost Sharing Rules, Serial Cost Sharing, Dominance Solvability.

Axiomatic Attribution for Multilinear Functions

We study the attribution problem, that is, the problem of attributing a change in the value of a characteristic function to its independent variables. We make three contributions. First, we propose a formalization of the problem based on a standard cost sharing model. Second, we show that there is a unique attribution method that satisfies Dummy, Additivity, Conditional Nonnegativity, Affine Scale Invariance, and Anonymity for all characteristic functions that are the sum of a multilinear function and an additive function. We term this the Aumann-Shapley-Shubik method. Conversely, we show that such a uniqueness result does not hold for characteristic functions outside this class. Third, we study multilinear characteristic functions in detail; we describe a computationally efficient implementation of the Aumann-Shapley-Shubik method and discuss practical applications to pay-per-click advertising and portfolio analysis.Comment: 21 pages, 2 figures, updated version for EC '1

A Theory of Attribution

Attribution of economic joint effects is achieved with a random order model of their relative importance. Random order consistency and elementary axioms uniquely identify linear and proportional marginal attribution. These are the Shapley (1953) and proportional (Feldman (1999, 2002) and Ortmann (2000)) values of the dual of the implied cooperative game. Random order consistency does not use a reduced game. Restricted potentials facilitate identification of proportional value derivatives and coalition formation results. Attributions of econometric model performance, using data from Fair (1978), show stability across models. Proportional marginal attribution (PMA) is found to correctly identify factor relative importance and to have a role in model construction. A portfolio attribution example illuminates basic issues regarding utility attribution and demonstrates investment applications. PMA is also shown to mitigate concerns (e.g., Thomas (1977)) regarding strategic behavior induced by linear cost attribution.Coalition formation; consistency; cost allocation; joint effects; proportional value; random order model; relative importance; restricted potential; Shapley value and variance decomposition