Cooperative game approaches to coordinating a three-echelon closed-loop supply chain with fairness concerns

This paper investigates a three-echelon closed-loop supply chain (CLSC) consisting of a manufacturer, a distributor, and a retailer, where the retailer exhibits fairness concerns. Cooperative and non-cooperative game theoretic analyses are employed to characterize interactions among different parties. Analytical results confirm the conventional wisdom: with the retailer's fairness concerns, the channel profits under the decentralized and partial-coalition models underperform that under the centralized model. To find an appropriate profit allocation scheme to coordinate the supply chain system with fairness concerns, we resort to the cooperative game theory. To this end, we first derive the characteristic function form of the cooperative game based on the equilibrium profits under centralized, decentralized and different partial-coalition models. Subsequently, we propose three coordination mechanisms based on the Shapley value, nucleolus solution, and equal satisfaction to allocate surplus profit. The three mechanisms are then evaluated by using numerical experiments. We further examine how the retailer's fairness concerns affect profit allocation under the three mechanisms. The key innovation is to incorporate the retailer's fairness concerns into the coordination of a three-echelon CLSC. Our contributions are twofold: First, cooperative game-theoretic mechanisms are put forward to coordinate the three-echelon CLSC with a fairness-minded retailer. Second, we investigate how the retailer's fairness concerns affect the CLSC members' pricing decision and surplus profit allocation. Our studies confirm that the resulting profit allocation schemes satisfy both individual and collective rationality and fall in the core of the cooperative game, thereby making the grand coalition stable and suggesting viable options to coordinate the CLSC system. Further analyses reveal that different coordination mechanisms benefit the three CLSC members differently. These research findings help CLSC managers to understand what options are available and identify possible pathways for them to foster cooperation and achieve equitable allocation of surplus profit.