Subsidized and unsubsidized price competition in a multi-echelon natural gas supply chain with governmental and private members

Determining the optimal prices among supply chain members, including both governmental and private natural gas producers, processing plants (PPs), and distribution centers (DCs) is an important and challenging task. This paper analyses the competitions between the members of a multi-echelon natural gas supply chain for determining their prices, which specify the demand for their products. This study proposes a novel game theory model to investigate cooperative and non-cooperative pricing scenarios. While, in Scenario 1, all supply chain members make decisions cooperatively as a centralized model, the members compete simultaneously to obtain the Nash equilibrium in Scenario 2. The Karush-Kuhn-Tucker (KKT) conditions are defined for the non-cooperative game and the Nash equilibrium is obtained using two different methods. The proposed model is applied to a realistic case study based on a data set derived from the natural gas industry to analyze the optimal pricing decisions under the two scenarios and verify the practicality of the proposed approach. Moreover, the variability in the profits of the members with respect to the changes in the base demands and self-price sensitivity parameters are studied. The results show that the government's total profit in the cooperative scenario is more than the non-cooperative scenario, while the profit of the private DC in the Nash equilibrium of the non-cooperative scenario is more than that of the cooperative scenario. Moreover, increasing the base demand for the private DC leads to a decrease and increase in its profit in Scenarios 1 and 2, respectively. These findings illustrate the potential sources of conflicts between governmental and private members of the natural gas supply chains when seeking collaboration to improve their profits and highlight the need for future research on incentive mechanism designs facilitating such collaboration.