Social responsibility inspiration in the fourth party logistics service supply chain: A game-theoretic approach

Corporate Social Responsibility (CSR) is considered in a fourth-party logistics service supply chain, consisting of a Fourth Party Logistics supplier (4PL) and a Third Party Logistics provider (3PL). In this research, a transportation price contract is designed to effectively improve the CSR performance, which is mainly determined by the 3PL's output of carbon dioxide (
$CO_{2}$
) emission. The associated cost for improving CSR performance level of the fourth-party logistics service supply chain is measured by a variable, which is only bring by the 3PL with an expectation of being shared with the 4PL via the transportation price contract. As such, the key issue is how the 4PL can identify the contract parameters to effectively transfer the associated cost of the 3PL in the 4PL service supply chain dominated by 4PL, and to encourage the 3PL to improve the performance level of CSR. A game-theoretical analysis is carried out on two games, bringing about different interaction plans between the 4PL and the 3PL, to derive their corresponding equilibria. Through the numerical analysis on the equilibria, we find that the 4PL service supply chain can achieve a win-win situation for both parties when the parameter values can be properly identified by the 4PL in designing the transportation price contract. Moreover, a well-designed contract can effectively motivate the 3PL to improve the performance level of CSR.