Trilateral game and vertical collaboration models in a two-stage green supply chain with substitutable green products

Abstract

This paper explores the trilateral game and vertical collaboration model based on Stackelberg’s (manufacturer-leadership game) and Bertrand’s game-theoretical methodology for a two-stage green supply chain where the duopolistic manufacturers and the retailer are ecologically conscious. Both manufacturers produce and sell two substitutable green products through a common retailer. The selling prices and green levels (GLs) determine the demand for both green products. A game theoretical approach is implemented in the trilateral game model, and the result shows that the manufacturer with a bigger sales volume achieves superior performance in terms of earnings. In the vertical collaboration model, a manufacturer and retailer collaborate to optimize pricing issues, GLs, and profits. Two-player games among three participants are performed for this collaboration. The results of the vertical collaboration model show that the overall profit in vertical collaboration is greater than the sum of the individual profits corresponding to two participants in the trilateral game model. Whereas, the manufacturer outside the collaboration experiences a decline in profits. Further, a selection criterion of manufacturers is also developed to maximize the overall profit of the retailer. Finally, a numerical example and a sensitivity analysis are performed to demonstrate the model’s implementation and stability.