Characterizations of the sequential equal contributions rule for the airport problem

The airport problem is concerned with sharing the cost of an airstrip among airlines who need airstrips of different lengths. We investigate the implications of various axioms specifying how a rule should respond to changes in the set of airlines for airport problems. Population fairness requires that upon the arrival of a new airline, the contributions of all airlines whose costs are not less than the cost of the new airline should be affected by equal amounts. Smallest-cost consistency requires that upon the departure of an airline with the smallest cost, if the problem is reevaluated from the viewpoint of the remaining airlines, then all the remaining airlines should contribute the same amounts as they did initially. Balanced population impact requires that the effect on the contribution from the departure of one airline to another should be the same between any two airlines. We show that each of these axioms together with other minor axioms characterizes the best-known rule for the problem, the sequential equal contributions rule.