A Generalized Cost Allocation Scheme

Abstract

This chapter presents a cost allocation scheme for a situation where there is a group of potential users of a common facility. In such as case, it can be supposed that some subcoalitions are not possible and, hence, the ordering of users is important. In such a case, not all orders of users within the group will be equally likely. The chapter presents a cost of allocation scheme by generalization of a few game theory concepts used in deriving the Shapley value and extending the probability notions used in Loehman and Whinston. The form of the Shapley value was derived in by first decomposing a game into subgames and then using some axioms to develop a value for a player in the game from this decomposition. The chapter highlights both decomposition of a game and the role of axioms but, at each point, generalizes the Shapley results by applying some concepts of linear algebra.