We study an original equipment manufacturer (OEM) purchasing two inputs for assembly from two suppliers with private cost information. The OEM can contract with the two suppliers either simultaneously or sequentially. We consider both cases in which the OEM has relatively equal bargaining power (the dynamic bargaining institution) or substantial bargaining power(the mechanism design institution). For the dynamic bargaining institution, we show that in sequential bargaining, the supply chain profit is higher, the OEM earns a lower profit, the first supplier earns a higher profit, and the second supplier may earn a higher or lower profit, than compared to simultaneous bargaining. For the mechanism design institution, we show that all players' profits are the same in simultaneous and sequential contracting. We also benchmark against a case where the OEM procures both inputs from a single integrated supplier (a dyadic supply chain). We then test these predictions in a human-subjects experiment, which support many of the normative predictions qualitatively with some deviations: an OEM with relatively equal bargaining power weakly prefers to contract with suppliers simultaneously while an OEM with substantial bargaining power prefers to contract with suppliers sequentially. In addition, the supply chain efficiency and the OEM's profit are higher in the dyadic supply chain than the assembly system.