With the rapid development of e-commerce platforms, more and more attention has been paid to the information asymmetry between the platform and upstream firms. This paper investigates the information-sharing strategy for an e-commerce platform on which two competing original equipment manufacturers outsource their manufacturing services to a common contract manufacturer and sell substitutable products directly to consumers. A game-theoretic model is employed to examine six information-sharing scenarios, and we derive the following results. First, the platform always voluntarily offers its demand information to other chain members when the contract manufacturer is the leader in the market. In particular, the platform obtains the most profit when it shares the information only with the contract manufacturer. Second, both the contract manufacturer and the original equipment manufacturers can benefit from information sharing. Information sharing can also help to increase the profit for the whole supply chain. Contrary to intuition, the whole supply chain is most profitable when the information is shared only with the contract manufacturer. Third, if the contract manufacturer gets the information, the profit for each member will increase with the demand forecasting accuracy. In addition, this paper explores the impacts of different leader–follower relationships on information sharing in the extension section. It is shown that when the original equipment manufacturers are the leaders and the contract manufacturer is the follower, the platform does not always share the information with others, and its information-sharing strategies change significantly.