Highlights • Competition of two freight transport systems with government intervention is assessed. • The interactions between the three dimensions of sustainability are investigated. • Government intervention can effectively eliminate rebound effects. • A practical solution is proposed to exempt the government from subsidy payment.

Abstract Sustainable freight transportation is a logistics approach that provides affordable services to consumers where environmental, economic, and social sustainability dimensions are concerned. Governments usually improve sustainability dimensions in freight transportation by imposing taxes on transportation systems. Therefore, they should extend their knowledge on interactions between sustainability dimensions and how their interventions affect each dimension. In this regard, we analyze competition between two freight transportation systems in the context of government intervention. These systems include road and intermodal road–rail transportation modes, where the latter is regarded as an environmentally sustainable mode. A sequential game is addressed to analyze the duopoly competition. In the upper level, a government, as a Stackelberg leader, imposes taxes on fuel usage based on environmental, economic, and social concerns. In the lower level, a Nash game is developed to analyze price competition in the transportation market. Our analyses reveal that: (a) Given a fixed level of the consumers' loyalty to their specific transportation systems, economic and social sustainability are consistent with each other, while they conflict with environmental sustainability. (b) Economic risks increase economic sustainability requested by the transportation systems. Such a relationship and the mentioned conflict between environmental and economic sustainability imply that a reduction of economic risks by the government indirectly contributes to environmental sustainability. (c) An increase in the consumers' loyalty simultaneously improves the three sustainability dimensions. (d) The energy efficiency improvements of the transportation systems may pose adverse environmental and social effects, called the rebound effects. Moreover, government intervention effectively eliminates such rebound effects. (e) Government support for the service enhancement of the intermodal system, combined with the national advertisement of this system, may exempt the government from subsidy payment.