The airport problem with capacity constraints

Abstract

The original airport problem is concerned with the cost sharing of an airstrip among airplanes assuming that one airstrip is sufficient to serve all airplanes. In this paper, we generalize the original airport problem by imposing capacity constraints to consider the situation when one airstrip cannot serve all airplanes and investigate how to share the cost among airplanes. We introduce the sequential equal contributions rule for our problem and show that it coincides with the Shapley value of the corresponding airport game when the worth of a coalition is defined to be the minimum cost of serving all members of the coalition. The sequential equal contributions rule requires each airplane to contribute equally to the cost of a given section of any airstrip as long as the length of the section is less than or equal to its desired length even though the airplane cannot use the airstrip. Each airplane’s contribution is the sum of terms, one for each section of the airstrip whose length is less than or equal to its desired length. We also present an axiomatic characterization of the rule by imposing the axioms of efficiency, the equal share lower bound, smaller-cost monotonicity, and population fairness.