We consider the outsourcing strategy problem of two competing original equipment manufacturers (OEMs) whose products are each made up of two components. The OEMs have different specializations, and therefore the component that each firm can produce in-house is different. Each firm must decide whether to outsource the other component to the competing OEM or to a third-party supplier. Prior research has demonstrated that competitors can be better off cooperating as supply-chain partners; therefore, one might expect that, as long as the OEMs are not at a severe cost disadvantage, they should maximize their cooperation as supply-chain partners, especially when competition between products is strong. Interestingly, this study finds that more cooperation between competitors may actually be harmful. Under certain conditions, while one of the OEMs should outsource to the competing firm, the other should outsource to a third-party supplier, even when the third-party supplier is more expensive and the competition is intense.