In this study, we consider different cities located along a tram line. Each city may have one or several stations and information is available about the flow of passengers between any pair of stations. A fixed cost (salaries of the executive staff, repair facilities, or fixed taxes) must be divided among the cities. This cost is independent of the number of passengers and the length of the line. We propose a mathematical model to identify suitable mechanisms for sharing the fixed cost. In the proposed model, we study, and characterize axiomatically, three rules, which include the uniform split, the proportional allocation and an intermediate situation. The analyzed axioms represent the basic requirements for fairness and elemental properties of stability.

In this paper we study the class of claims problems where the amount to be divided is perfectly divisible and claims are made on indivisible units of several items. Each item has a price, and the available amount falls short to be able to cover all the claims at the given prices. We propose several properties that may be of interest in this particular framework. These properties represent the common principles of fairness, efficiency, and non-manipulability by merging or splitting. Efficiency is our focal principle, which is formalized by means of two axioms: non-wastefulness and Pareto efficiency. We show that some combinations of the properties we consider are compatible, others are not.