Sharing benefits in an airlines problem

G. Bergantiños Cid, L. Lorenzo Picado

Airlines form alliances to expand their network, cut costs, and enhance services, increasing overall profitability. Thus, a fair profit-sharing mechanism is essential for long-term cooperation.
Two allocation methods are proposed: the Flight Proportional Rule and the Distance Proportional Rule, which aligns with the IATA Proportional Mileage Principle. The first rule is characterized by means of additivity, independence of empty flights, independence of other airlines, and flights equivalence; while the second is characterized by additivity, independence of empty flights, and distance equivalence.
Additionally, we associate a cooperative game with each airlines problem. We characterize the Shapley value with additivity, independence of empty flights, and passengers symmetry. Finally, we prove the allocations in the core are those where the fare paid by each passenger is divided among the airlines operating their flights, and each airline receives the sum of its corresponding shares.

Keywords: Alliances, benefit sharing, cooperative game theory

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