Bargaining under Incomplete Information, Fairness, and the Hold-Up Problem ∗

In the hold-up problem incomplete contracts cause the proceeds of relation-specific investments to be allocated by ex-post bargaining. The present paper investigates the efficiency of incomplete contracts if individuals have heterogeneous preferences implying heterogeneous bargaining behavior and- equally important- preferences are private information. As the sunk investment costs can thus potentially signal preferences, they can influence beliefs and consequently bargaining outcomes. The necessities of signalling are shown to generate very strong investment incentives. These incentives are based on the desire not to reveal information that is unfavorable in the ensuing bargaining. After finding all perfect Bayesian equilibria in pure strategies, the paper derives the necessary and sufficient conditions under which it is optimal to invest and trade efficiently