Game theory model for sustainable multi-modal freight transport: Balancing competition among risk-averse 3PLs and government intervention

Third-party logistics providers (3PLs) play a vital role in freight transportation supply chains (SC) and face intense competition to stay profitable. As a result, making well-informed decisions is crucial for their success. This study examines a 3PL that operates a railway fleet alongside competing 3PLs that rely on road transportation. While all 3PLs compete to secure cargo, those using road transport also face the challenge of attracting drivers amidst ongoing driver shortages. To address this, a risk-aversion model is developed for 3PLs. The study also considers a fuel refinery that supplies both biofuel and fossil fuel to meet the needs of road and rail transport. The refinery has the option to export surplus fuel to external markets at a premium price. Meanwhile, the government plays a key role by subsidizing biofuel supply and regulating greenhouse gas emissions from fuel production through penalties. A sustainable SC is achieved through a Nash equilibrium, with the government acting as the leader in a Stackelberg game framework. Prices and other decision variables are determined by optimizing each stakeholder's objective function, while the government's function is designed to ensure SC sustainability. Additionally, special emphasis is placed on promoting rail transport as an environmentally friendly alternative. The model's validity is demonstrated through a real-world case study and sensitivity analysis. Results indicate that government intervention supports SC sustainability by encouraging both rail transport and biofuel production, with biofuel optimized to account for 17.15 % of the total fuel supply on average. By implementing subsidies and improving logistics services, competition among 3PLs can drive higher rail fleet utilization, reaching up to 78 % of total fleet use.