Non-cooperative and Nash-bargaining game of a two-parallel maritime supply chain considering government subsidy and forwarder's CSR strategy: A dynamic perspective

In recent years, sustainable and environmental issues have increasingly raised concerns of the government and enterprises. Motivated by the environmental regulations of IMO and shippers' green preferences, new energy vessels (NEV) have been developed, and there are still many traditional fuel vessels (TFV) providing maritime transport services. Considering the reality of the shipping market, a two-parallel maritime supply chain (MSC) involving a NEV carrier, a TFV carrier, and a freight forwarder with corporate social responsibility (CSR) has been constituted. The government may encourage the NEV carrier to make green innovation (GI) by providing subsidies. Most existing research on supply chain decisions considered different supply chain power structures or coordination issues and assumed that enterprises are entirely rational. However, in practice, bargaining games between stakeholders are common. Consequently, non-cooperative game (NCG), two types of Nash-bargaining game, i.e. horizontal Nash-bargaining game (HNBG) and vertical Nash-bargaining game (VNBG) are formulated in this paper. Based on bounded rationality, we investigate the dynamic price and GI adjustment strategies of MSC participants under government subsidy (GS) and freight forwarder's CSR (FCSR) with three game patterns. Furthermore, the impacts of adjustment parameters, GS, and FCSR on equilibrium strategies and expected profits are also explored. Setting NCG as the benchmark case, we uncovered that both HNBG and VNBG help improve the NEV carrier's equilibrium green innovation level (GIL), and HNBG (VNBG) raises (lowers) equilibrium prices of two carriers (freight prices and selling prices). In addition, HNBG (VNBG) can stabilize the adjustment of GI (freight prices and selling prices). For all MSC participants, excessive adjustment strategies harm robust revenues. We also found that GS and FCSR have different impacts on the dynamic decision-makings. When adjustment parameters are in their stable regions, GS always benefits the NEV carrier and the freight forwarder. But the impact of GS on the TFV's revenues may be related to the intensity of FCSR. Moreover, the effect of FCSR on stakeholders' expected profits depends on the choice of game pattern. Finally, we revealed that the TFV carrier's CSR-sharing behavior helps improve the stability of the MSC dynamic decisions and promotes the mutual benefit of MSC participants.