Applying an axiomatic approach to revenue allocation in airlines problems

The International Air Transport Association (IATA) states that the revenue from interline tickets must be shared among the different airlines according to a weighted system. We analyze this problem following an axiomatic approach, and our theoretical results support IATA’s procedure. Our first result justifies the use of a weighted system, but it does not specify which weights should be applied. Assuming that the weights are fixed, we provide several results that further support the use of IATA’s mechanism. Finally, we provide results for the case in which all flights can be considered equivalent and no weighting is required.

💡 Research Summary

The paper investigates the problem of allocating revenue from interline airline tickets among the participating carriers, a task governed in practice by the International Air Transport Association (IATA) through its Multilateral Prorate Agreement (MPA‑P). The authors adopt an axiomatic framework to assess whether IATA’s weighted‑proration mechanism is theoretically justified and to explore which alternative rules might be appropriate.

First, a graph‑theoretic model is introduced. Airports are vertices, directed edges represent possible flight legs, and each edge may be operated by several airlines. A finite set of passengers is specified, each passenger being associated with a path (itinerary) through the graph and a fare amount (net of taxes and fees). The total revenue to be divided is the sum of these net fares.

The authors propose four fundamental axioms that any reasonable allocation rule should satisfy:

1. Additivity – the allocation for a set of passengers equals the sum of the allocations for each passenger taken separately.
2. Null airline – an airline that carries no passengers receives zero revenue.
3. Independence of other airlines – the amount received by an airline depends only on the flights it operates, not on which other airlines operate the remaining flights.
4. Ratio preservation – if two passengers share the same set of flights and airline i receives λ times more than airline i′ from the first passenger, the same λ factor must hold for the second passenger.

The authors prove that any rule satisfying these four axioms must be a weighted‑flights rule: each airline’s share is proportional to the sum of the pre‑specified weights of the flights it operates. This result validates the general structure of IATA’s proration system, which indeed distributes revenue proportionally to weighted flight factors. However, the axioms alone do not determine the specific numerical weights.

Assuming the weights are exogenously fixed (as they are in the IATA practice), the paper introduces three additional axioms:

• Pairwise homogeneity – if for every passenger the ratio of the weights of two airlines’ flights is constant, then the total revenue received by those airlines must preserve that same ratio.
• Independence of empty flights – removing a flight that carries no passengers does not affect any airline’s allocation.
• Flights equivalence – when all flights are considered identical (i.e., all weights are equal), the allocation should be proportional solely to the number of flights each airline operates.

Using different combinations of these axioms, the authors obtain three distinct characterizations of the weighted‑flights rule. Two of them combine additivity and pairwise homogeneity with either the null‑airline axiom or the independence‑of‑empty‑flights axiom. The third characterization, which also incorporates the flights‑equivalence axiom, yields the equal‑flights rule: revenue is divided proportionally to the count of flights contributed by each airline when all flights are deemed equal. This rule is particularly relevant for markets where flight characteristics (distance, cost structure, etc.) are relatively homogeneous.

The paper then details the actual IATA proration procedure. IATA first computes a “prorate amount” by stripping taxes and ancillary charges from the ticket price. It then assigns a Ticketed Point Mileage (TPM) to each leg, multiplies TPM by a “Worldwide Weight” (given by the formula 6.338826 × TPM − 0.209892), and finally applies regional correction factors that reflect operating costs, market conditions, and policy considerations. The resulting Standard Proration Factor (SPF) is rounded to an integer, and each airline receives a share of the prorate amount proportional to the sum of its SPF values across the passenger’s itinerary. The authors illustrate the process with a Madrid‑Frankfurt‑Nairobi example, showing how the weighted approach mitigates the bias that would otherwise favor longer segments.

In the literature review, the authors contrast their work with previous game‑theoretic studies of airline revenue sharing (e.g., Shapley value, nucleolus, core allocations). Those studies often assume restrictive network structures (trees) or single‑airline operation on each leg, whereas the present model accommodates arbitrary graphs, multiple airlines per leg, and realistic multi‑leg itineraries. The axiomatic perspective also aligns with recent research on resource‑allocation axioms in other domains (pandemic indicators, liability sharing, content creator payments).

The concluding section emphasizes three main contributions: (i) a rigorous axiomatic justification for the weighted‑proration framework used by IATA; (ii) a set of additional axioms that uniquely characterize both the weighted‑flights rule (for any fixed weight system) and the equal‑flights rule (when all flights are homogeneous); and (iii) a bridge between practical industry practice and formal economic theory, offering guidance on how weight‑selection should be performed to satisfy the identified axioms. By demonstrating that IATA’s current mechanism satisfies the core axioms, the paper supports the fairness and stability of revenue sharing in airline alliances while also highlighting the importance of transparent, theoretically grounded weight updates.