We consider a decentralized supply chain in which a downstream manufacturer purchases components from an upstream supplier privileged with private information about supply disruption risk. The supplier's initial reliability, asymmetric to the manufacturer, is either low or high. We examine two representative contracts, i.e. the wholesale price and screening menu contracts. Under the wholesale price contract, we specify two practical regimes: pull and push. We derive and compare the firms' equilibrium solutions, profitability, and channel performance in these two regimes. We find that in the push regime the payoff of either the high- or low-reliability supplier monotonically increases with their initial reliability, while the manufacturer's payoff remains constant if the reliability enhancement cost is small; otherwise it will also monotonically increase. By contrast, in the pull regime, the manufacturer's payoff will always increase, while the supplier's payoff is non-monotonic with their initial reliability. We further show that the manufacturer's payoff is non-increasing with the initial reliability heterogeneity in both the push and pull regimes. Under the screening menu contract, we also consider two regimes: contracting both high- and low-reliability suppliers, and contacting just the high-reliability supplier, respectively, and we derive the equilibrium solutions in each regime. The results reveal that the regime of contracting both suppliers dominates the regime of contracting only the high-reliability supplier under a certain condition. Comparing the wholesale price and screening menu contracts, we derive several interesting results. First, when either the reliability enhancement cost or initial supply reliability heterogeneity is sufficiently high, the pull regime is dominant for the manufacturer; the regime of contracting both suppliers is more favorable to the manufacturer when the reliability enhancement cost and initial supply reliability heterogeneity are low. Second, in the pull regime, more information transparency is detrimental to the manufacturer's payoff when the supplier's initial reliability is low, whereas the high-reliability supplier will surprisingly yield a higher profit under information symmetry. Third, the low-reliability supplier's preference on information transparency hinges on the enhancement cost coefficient in the push regime
