Financial Cost Allocations: A Game-Theoretic Approach

In two research studies published by the American Accounting Association � Arthur L. Thomas concludes that financial cost allocations are not only arbitrary but also incorrigible, i.e., incapable of veri-1 fication or refutation by reference to external "real world " phenomena. While maintaining that the logic can be generalized to all financial cost allocations, Thomas particularizes his argument to depreciation allocations. Either depreciation allocations are essentially arbitrary because they have no theoretical justification, Thomas contends, or they are ' predicated on a net-revenue-contributions (NRG) approach. The latter appears to be justifiable since the resulting allocation pattern follows the expected net revenue contributions of the asset or project to the firm-entity. However, even NRG allocations cannot be justified if the inputs to the revenue generating process interact to produce the revenues of the firm. Unless the inputs operate independently of each other, the allocation of depreciation over time must result in the arbitrary allo-cation of a joint cost to a specific asset. Since there is no unique and identifiable cause-and-effect relationship between a specific asset and t9e revenues generated by interacting assets, any and all allocations are equally justifiable and, therefore, incorrigible.2 In this paper we hope to demonstrate that, by employing certain elementary game-theoretic concepts, financial accounting allocations need not be arbitrary nor incorrigible even though asset interactions are prevalent. In what follows, Section I illustrates Thomas ' argument in a simple depreciation allocation example. Section II introduces the concept of a Shapley value and applies it to our example. Finally, Section ILI concludes that Shapley values represent a defensible and corrigible cost allocation mechanism