A Game Theoretical Approach to Optimize Policies of Government Under the Cartel of Two Green and Non-green Supply Chains

In this research, firms aim at maximizing two purposes of social welfare (environment) and profitability in the supply chain system. It is assumed that there are two supply chains, a green and an ordinary, each consists of a manufacturer and a supplier; in which the manufacturer generates profit through franchises. The green and the ordinary manufacturers form a cartel on the market of a certain product with the goal of increasing their mutual profits and maintaining a certain level of social welfare, while the government, as a leader, intervene financially using tax rates and incentives. We formulate the problem as a Stackelberg game model seeking the equilibrium solutions. A numerical example is presented and a sensitivity analysis is carried out. The results show that the investment’s encouraging tax rate in green technology has no impact on the optimal production of the green and ordinary manufacturers. Therefore, it is not an affective variable on the product market, but it is an important variable for the state utility function. Another highlight is that if tax rates are not equal for green and ordinary goods, then either the green or the ordinary producer will be withdrawn from the market. The most important result of this study is that if the government wants to maximize its utility function when the final product’s market is facing with a cartel and the price collusion between the green and ordinary producer, it should realize the equality between the ordinary and green tax rate and there is no difference between these two parameters of the government's decision. If the government is willing to keep the green producer in the market, the optimal and absolute tax rate of green chain is obtained by assuming zero profit of the green manufacturer.