ON COST ALLOCATION IN COMMUNICATION-NETWORKS

We consider two cost allocation problems that arise when the prospective users of a communication network seek a fair method for allocating the cost of constructing the network. We assume the network is of minimum cost and its edge capacities are large enough to satisfy requirements for every pair of users. If the requirements are time‐invariant and have to be satisfied simultaneously, the problem of finding a minimum‐cost network is called the simultaneous network synthesis problem, whereas if the requirements can be satisfied for one pair of users at a time, it is called the nonsimultaneous network synthesis problem. We formulate the cost allocation problems arising from the above problems as cooperative games, referred to as the simultaneous and the nonsimultaneous network synthesis games. We prove that both the (equal cost) nonsimultaneous and the simultaneous network synthesis games are convex and provide nonredundant representations of their cores. For the simultaneous network synthesis game, we present a closed‐form expression for the nucleolus and prove that it coincides with the Shapley value. For the (equal cost) nonsimultaneous network synthesis game, we, provide a closed‐form expression for the nucleolus when the requirement structure is tree‐shaped and develop a quadratic time algorithm for computing the Shapley value in this case. Copyright © 1990 Wiley Periodicals, Inc., A Wiley Company