Proportional allocation schemes for tour costs (Q1820664)

This paper examines the problem of allocating intercity travel costs for a multicity trip to sponsors at the different cities in as fair a manner as possible when each sponsor is willing to pay as much as the round-trip cost between his city and the traveler's home. Intercity travel costs are presumed to satisfy the usual triangle inequality. The paper first considers a fixed-route situation and shows that four axioms - including full cost recovery, monotonicity and additivity conditions - delineate a simple class of allocation schemes. All possible tours through the cities are then admitted under a fifth axiom which says that minimum-cost tours are Pareto optimal for the sponsors. This efficiency axiom further restricts the class of allocation schemes, but it does not force a unique result. Additional conditions that do in fact identify a unique scheme are mentioned. A relaxation of the triangle inequality for costs is also discussed.