Three rules for airport problems: Characterizations via order preservation, dispersion minimization, and consistency

We consider a class of cost allocation problems where a public facility is shared by a group of agents with “needs” for it, and these needs possess a “nested” character. A facility accommodating an agent can also accommodate any other agent with a lower need at no extra cost. The facility has to be provided to accommodate all agents. The question is how to allocate its cost among them. An example is airlines sharing an airstrip. These problems are therefore known as “airport problems”. We identify desirable rules through the axiomatic approach. We propose three main axioms: (i) order preservation in contribution rates, which requires the order of agents’ contribution rates to match the order of their needs; (ii) minimizing the range of contribution rates, which requires that the difference between the highest and lowest contribution rates among agents be minimized; and (iii) single-constraint consistency, which is an expression of the well-known “consistency” principle. Drawing inspiration from the literature on economic design, we adapt the proportionality principle to guarantee that no group of agents subsidizes the complementary group. We call this resulting rule the “constrained proportional rule”. Our main result is that this rule is the only rule satisfying these three axioms. We also provide new characterizations of two other well-known rules. The “constrained equal contributions rule” is the only rule minimizing the variance of contributions. The “constrained equal benefits rule” is the only rule minimizing the range (or variance) of benefits.