In this paper, the competition between two supply chains and their elements is studied. Each chain consisted of a manufacturer and a distributor and the two chains compete in a market with single type of customer sensitive to price and delivery time. Therefore, this is a two-supply chain game and during the competition between two supply chains, elements of each supply chain (manufacturer and/or distributor) may follow either centralized or decentralized strategy; i.e. within each supply chain the elements may choose to cooperate or compete in order to achieve more profit. Combined strategies between two supply chains and their elements are of four types: i. both chains apply centralized policy; ii. The first chain chooses centralized and the second one follows decentralized policy; iii. The first chain applies decentralized and the second one chooses centralized policy; iv. Both chains follow decentralized policy. The competition between two chains was analyzed as a Stackelberg game and without loss of generality supposing that the first chain acts as leader and the second one is the follower. The profit earned by each supply chain is related to the aforementioned combination of strategies chosen by each supply chain. Finally numerical examples are provided to investigate these strategies and to determine the best combined strategy by comparing the profit of chain elements and whole profit of each chain.