Vì vậy, Ramsey giá có thể ở dưới chi phí cận biên nếu một số dịch vụ bổ sung . Ví dụ, nếu n D 2, và độ co giãn không đổi, với các giá trị của , sau đó chúng ta có thể dễ dàng tính toán rằng . Là một minh họa này, xem xét một trường hợp của hai dịch vụ, thoại và video. Có nhu cầu về giọng nói một mình, cho video một mình, và cho thoại và video | FOUNDATIONS OF COST-BASED PRICING 171 aggrieved unless he benefits at least as much from customer i s presence. So again we must have . Surprisingly there is only one function Ộ which satisfies for all T N and i j 2 T. It is called the Shapley value and its value for player i is the expected incremental cost of providing his service when provision of the services accumulates in random order. It is best to illustrate this with an example. Example Sharing the cost of a runway Suppose three airplanes A B C share a runway. These planes require 1 2 and 3 km to land. So a runway of 3 km must be built. How much should each pay We take their requirements in the six possible orders. Cost is measured in units per kilometer. Order Adds cost A B C A B C 1 1 1 A C B 1 0 2 B A C 0 2 1 B C A 0 2 1 C A B 0 0 3 C B A 0 0 3 Total 2 5 11 So they should pay for 2 6 5 6 and 11 6 km respectively. Note that we would obtain the same answer by a calculation based on sharing common cost. The first kilometer is shared by all three and so its cost should be allocated as 1 3 1 3 1 3 . The second kilometer is shared by two so its cost is allocated as 0 1 2 1 2 . The last kilometer is used only by one and so its cost is allocated as 0 0 1 . The sum of these vectors is 2 6 5 6 11 6 . This happens generally. Suppose each customer requires some subset of a set of resources. If a particular resource is required by k customers then under the Shapley value paradigm each will pay one-kth of its cost. The intuition behind the Shapley value is that each customer s charge depends on the incremental cost for which he is responsible. However it is subtle in that a customer is charged the expected extra cost of providing his service incremental to the cost of first providing services to a random set of other customers in which each other customer is equally to appear or not appear. The Shapley value is also the only cost sharing function that satisfies four axioms namely 1 all players are .
