Capacitated Network Design Games on a Generalized Fair Allocation Model

The cost-sharing connection game is a variant of routing games on a network. In this model, given a directed graph with edge costs and capacities, each agent wants to construct a path from a source to a sink with low cost. The cost of each edge is shared by the users based on a cost-sharing function. One of simple cost-sharing functions is defined as the cost divided by the number of users. It models an ideal setting, where no overhead arises when people share things, though it might be quite rare in real life. In this paper, we model more realistic scenarios of cost-sharing connection games by generalizing the cost-sharing function. The arguments do not depend on specific cost-sharing functions and are applicable for a class of all natural cost-sharing scenarios, which include equal divisions with any natural functional overheads. We show that many bounds of the Price of Anarchy and the Price of Stability under sum-cost and max-cost criteria inherit the no-overhead case.