The Shapley Value As Applied to Cost Allocation: A Reinterpretation

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The problem of cost allocation is inescapable in virtually every organization and consequently pervades every facet of accounting. As an alternative to traditional accounting allocation bases, there is a growing interest in cost allocation schemes predicated on notions in game theory. Shubik [1962] was among the original proponents of this. He suggested the Shapley value as a method of joint-cost allocation, and it is the Shapley value that has continued to attract the widest interest.' The Shapley value was introduced by Shapley [1953] as a method for each player to assess a priori the benefits he would expect from playing a game. To show its application to the problem of assigning joint cost, let us suppose that the full cost of some common service (e.g., a computer facility, a power plant, or a maintenance staff) is to be shared among n departments, which will be designated by N = {1, 2, ..., n}. The function v( S) describes the net total benefit to the coalition S when those departments cooperate to secure the common service. For purposes of this discussion, it will be assumed that the total net benefit is expressed in