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Cooperation between upstream suppliers and downstream manufacturers in technology investment is a popular way to improve production technology for reducing suppliers' production costs of key components. Technology investments undertaken by manufacturers and wholesale price discount contract provided by suppliers have an important impact on their cooperation. This paper explores whether a supplier should cooperate with two downstream competing manufacturers to accept their technology investments to reduce the supplier's production cost of a key component. Specifically, we consider the following three cooperation strategies: the supplier does not accept manufacturers' technology investments, only accepts one manufacturer's technology investment and accepts both manufacturers' technology investments. Our results demonstrate that the wholesale price discount contract and the technology investment can enhance the profits of the supplier and two manufacturers when the discount degree is low. Further, we conclude that when the discount degree is relatively low or when the discount degree and the technology investment efficiency are relatively high, the supplier's optimal cooperation strategy with two manufacturers is to accept both manufacturers' technology invest-