A game theoretic model for dual supply chains with green and non-green products and bi-directional free-riding and carbon policy

Cap-and-trade regulation is a strategy to reduce carbon emissions (CEs). During production, CEs are reduced by green technology. In a dual-channel supply chain (DCSC), customers try a product at an offline store but purchase it online (showrooming effect). Additionally, using internet information services, some customers purchase offline (ropo effect). Due to demand uncertainty, neutrosophic fuzzy sets are used to appropriately express a parameter's impreciseness. We develop a game-theoretic model where a manufacturer produces non-green and green products using carbon reduction technology, sells the products through a traditional retailer (offline), and owns an online channel for imprecise market demands. Customers free-ride from both the channels. The CE from transportation and the non-green products are considered. For carbon costs, a cap and trade policy is adopted. The neutrosophic fuzzy variables indicate the impreciseness of the demand, bidirectional free-riding, and product greenness. These variables determine channel members' truth, indeterminacy, and falsity degrees. Different models with some prices (inconsistent and consistent) and service efforts as decision variables are analyzed using the Stackelberg game approach. After the derivation of the corresponding equilibrium equations, numerical experiments are presented to verify the validity of our conclusions. The findings show that although free-riding is detrimental to the retailer, it becomes advantageous if its direction is altered. The profit of the retailer with consistent prices is higher than the inconsistent one. Opposite outcomes are observed for the manufacturer. The channel members' profits are more under the neutrosophic fuzzy environment than deterministic/fuzzy. Some managerial insights and conclusions are presented.