A simple game theoretical analysis for incentivizing multi-modal transportation in freight supply chains

Multi-modal transportation, as a highly efficient approach, can economize many intermediate links in the supply chain and save social operating costs. However, at present, multi-modal transportation accounts for only a small portion of the total traffic volume, and there are few multi-modal carriers. To analyze the incentives of ocean shipping companies to provide multi-modal transportation, this paper considers a freight supply chain composed of two upstream ocean shipping companies and two downstream railway transportation companies. After depicting a Nash game between the two competing ocean shipping companies in terms of whether to integrate downstream railway transportation services to provide multi-modal transportation, we analyze the performance of the participants in sub-games for each integration strategy. The results indicate that regardless of competitor behavior, ocean shipping companies may have an incentive to provide multi-modal transportation. Although the two ocean shipping companies are unlikely to agree on the optimal strategy, the only effective equilibrium they can achieve is both providing multi-modal transportation. Moreover, in this equilibrium, the supply chain’s profit, consumer utility and social welfare are likely to be maximized. In addition, although the provision of multi-modal transportation will attract more shippers to the market, whether more shippers can ultimately be retained depends on the integration efficiency and competitive intensity.