Pricing decision is one of the most important factors in the supply chain management. If demand is sensitive to the price, pricing decision becomes more important. In this case, with a slight change in the price of products or services, the customer changes his demand that impact on chain profit. In this competitive environment, game theory is a Powerful tool for decision making. In this study, a supply chain consists of two exclusive traort companies and a retail company is taken into consideration. Each member of system will affect price and then affect profit of chain. We investigate three states in this study. First case discussed is centralized decision-making that a decision-maker determines prices of all chain. Then, a case studied that exclusive carriers with equal power as the leader and retailer as follower come into game. Finally we investigate a case that carriers as a centralized unit lead the market and retailer is follower. Traort companies have a unique feature that makes them exclusive company. Companies that traort hazardous chemical material, cargo liner companies in Iran and very large cargo traort company that can be examples for this situation in problem. The traort company can be a trucking company, a third-party logistics provider, or a freight forwarder. The retailer sets the retail price; this specifies the demand, which in turn, is the carrying amount for the traorters. Traorters decide the freight rate and their profit depend on both the freight rate and the carrying amount. Finally, the traorter’s freight rate is an input of the retailer’s cost that influences the retail price eventually. In this study the traortation cost divided into two category including costs per unit of goods such as load, unload and handling; and the fix cost per vehicle. The fixed cost includes the driver’s salary, fuel charges, etc. We entered cost per truck separately in traorters profit function that eventually led to integer linear model. In this study new heuristic and exact methods are developed to solve the problem. Due to the exclusive traort companies, a linear bilateral monopoly demand function will be introduced. After that, different sensitive analysis are illustrated for profit function graph. Finally, providing some examples, utility functions and variables in different scenarios will be examined. We found that, parameters related to fixed costs in specific rang have a significant impact on the profit. In general, the results showed a profit in centralized state more than other states. In Stackelberg-centralized state lowest supply chain profit and highest prices was achieved.