Problem definition: We consider a buyer sourcing from multiple competing suppliers who exert cost-reduction efforts before procurement contracts are awarded. Academic/practical relevance: The supply chain is subject to the classic hold-up problem—as the lack of a contract commitment hinders suppliers’ incentives to make investment upfront—complicated with supplier competition. Methodology: With deterministic cost-reduction outcomes, suppliers will not exert any effort if this effort is observable, and a pure-strategy equilibrium does not exist if the effort is unobservable. We analyze the mixed-strategy equilibrium with unobservable supplier effort, in which suppliers randomize their efforts and the buyer designs an optimal procurement mechanism. Results: We show that the optimal procurement mechanism can be implemented by a conventional single-price reverse auction with a random reserve price. The mixed strategy of supplier effort generates endogenous information asymmetry on supplier costs that provides suppliers with information rent, which sustains their efforts. The endogenous information asymmetry improves effort efficiency (by inducing positive supplier effort), yet introduces trade inefficiency (by causing the possible failure of trade between the parties). Although increasing supplier competition (measured by the number of suppliers) hurts the effort efficiency, it improves trade efficiency. As a result, the buyer is always better off introducing supplier competition by including more than one supplier in the supply base. However, the desired supply base size (number of suppliers) depends on the product revenue: For high-margin goods, the optimal size is achieved with two suppliers, whereas for low-margin goods, a larger supply base is better for the buyer. We show that the result based on deterministic cost reduction can be established as a limit of the case when uncertainty in cost reduction exists and shrinks to null. Managerial implications: Our study helps to understand the impact of supplier competition when supply-chain parties deliberately make their actions unpredictable to avoid being held up. The findings provide managerial guidance on procurement auction and supply base designs.