To purchase or to sell: Capacity agreement in high-speed railway and airline cooperation

High-speed railways (HSR) and airlines can complement each other in long-distance journeys served by connecting flights through a hub. To encourage airline-HSR cooperation and promote intermodal transport services, we examine two capacity agreements under the capacity limitations of HSR and/or airlines and their effects on ticket pricing, passenger volume, travel time, frequency, consumer surplus, social welfare, and profitability. In a capacity sell agreement, HSR sells its capacity to airline (HSA), and airline provides the bundling service. In a capacity purchase agreement, HSR purchases airline capacity (HPA) and offers the bundled service. We first analytically compare two capacity agreements with no-cooperation cases, and find that the joint ticket price under the HSA agreement offers a price advantage over individual ticket purchases in non-cooperation scenarios only when HSR is capacity-constrained. Although the HPA agreement also exhibits a similar joint price advantage as the HSA agreement, it requires the stringent condition that both transport modes have limited capacities. Regarding consumer surplus, it tends to increase under the HSA agreement when both transport modes have capacity limitations or both do not have capacity limitations. However, the increasing trend can be relaxed to different capacity limitation conditions under the HPA agreement. We then directly compare the HSA and HPA agreements through simulations. The results indicate that the HSA agreement yields higher consumer surplus and profits than the HPA agreement, while the HPA agreement achieves greater social welfare.