Supply chains today routinely use third parties for many strategic activities, such as manufacturing, R&D, or software development. These activities often include relationship-specific investment on the part of the vendor, while final outcomes can be uncertain. Therefore, writing complete contracts for such arrangements is often not feasible, but incomplete contracts, especially when relationship-specific investment is required, may leave the supplier vulnerable to a version of the 'hold-up problem,' which is known to result in sub-optimal levels of investment. We model the phenomenon as a sequential move game with asymmetric information. Absent behavioral considerations, the unique Perfect Bayesian Equilibrium implies zero investment. However, with social preferences, the hold-up problem may be mitigated. We propose a model that incorporates social preferences and random errors, and solve for the equilibrium. In addition, we look at reputation and find it to be effective for increasing investment. We conduct laboratory experiments with human subjects and find that a model with social preferences and random errors organizes our data well.