Sharing the Cost of a Path

Abstract

In recent years, many authors have analyzed fair division aspects in problems containing network structures. Frequently, the connection of all vertices of the network, that is, a minimum cost spanning tree, and the sharing of its cost was considered. In this article, we study the fair division of costs of connecting two designated vertices by a path. Specifically, we will introduce two cost-sharing rules that provide a division of the costs of forming a shortest path. One of the cost-sharing rules will include aspects from non-cooperative extensive form games in the sense that selfish and individually rational behaviour without agreement between the agents in a sequential structure is taken into account for the determination of the cooperative solution. The other cost-sharing rule is based on an alternating structure along the shortest path. Axiomatic characterizations of the two cost-sharing rules are provided.