optimal pricing strategy and cooperation in the supply chain with one direct selling manufacturer and duopoly retailers

Corresponding to the advent of technology, manufacturers are taking into consideration novel means of selling their respective products directly to the customer. thus, the present paper aims to find the optimal pricing strategy for a supply chain, including a single manufacturer and two retailers. in the proposed model, the manufacturer decides whether to consider the channel for his/her direct sales on the market. three scenarios are considered: lack of cooperation between retailers, cooperation between retailers with fixed-price sales, and cooperation between retailers with various sales prices. stackelberg game is used to examine scenarios in which the manufacturer is a leader, and two retailers pose as followers. in case of no cooperation between retailers, the results demonstrate a higher rate of profit for the manufacturer, while the total profit of the retailers is greater in the event of cooperation, using different sale prices. finally, a numerical example is provided in order to demonstrate the effectiveness of the aforementioned three scenarios in supply chain models.