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Quantum games is a relatively new inter-disciplinary research field in theoretical physics and game theory. It tries to resolve issues like "Prisoner's Dilemma" from classical games and improve efficiency of a game by applying quantum rules and assumptions to it. In this paper we study the effects of "sales integration" in Iran's petrochemical products on the profit of petrochemicals industry by using a quantum game model. At present, there are over 50 petrochemical factories in the country that all of them are owned by private sector. These factories were selling their products in an integrated framework through a government-owned commerce company until 2008, when they were privatized. The results show that integration of petrochemical products sales can improve the profitability of the companies individually and as a whole industry.