Mass balance or book and claim? Capacity allocation of sustainable aviation fuel among competing airlines

Sustainable Aviation Fuel (SAF) is widely regarded as a key solution for reducing aviation emissions. However, global SAF production capacity remains limited, making the allocation of scarce SAF among competing airlines a central challenge in the SAF supply chain. Different chain-of-custody (CoC) models impose different compliance requirements on airlines, which in turn affect capacity allocation and supply chain decisions. This paper focuses on two major CoC models, mass balance (MB) and book-and-claim (BC). Under MB model, SAF attributes must remain linked to physical SAF through bookkeeping. Under BC model, airlines can claim environmental benefits by purchasing SAF credits without physically using SAF on their flights. We mainly examine how the MB and BC models shape the allocation of limited SAF capacity. We develop a game-theoretic model consisting of a government, a single capacity-constrained SAF supplier, and two airlines with different ordering priorities, where the supplier allocates limited capacity according to lexicographical order. This paper shows that under the MB model, limited capacity enables the high-priority airline to monopolize the entire SAF capacity and gives the SAF supplier strong pricing power. In contrast, the BC model not only provides airlines with an additional compliance approach but also reduces the SAF supplier's pricing power and promotes a more reasonable allocation of capacity through strategic threats. Furthermore, we find that such strategic threats do not necessarily improve total supply chain profit but can enhance social welfare by reducing carbon emissions. Finally, several extensions demonstrate the robustness of our main findings.