Two-sided unobservable investment, bargaining, and efficiency

Asymmetric information can lead to inefficient outcomes in many bargaining contexts. It is sometimes natural to think of asymmetric information as emerging from imperfect observation of previously taken actions (e.g., obtaining compliments or substitutes for the item being bargained over). How do such strategic investment choices prior to bargaining interact with the strategic problem of bargaining under private information? We focus on bilateral bargaining when players can make unobserved investments in the value of the item prior to their interaction. With two-sided hidden investment, strategic uncertainty induces a post-investment problem analogous to that in Myerson and Satterthwaite (J Econ Theory 29(2):265-281, 1983), and inefficiencies might be expected to arise. But, there are strong incentives to avoid investment levels that do not lead to trade and this must be anticipated by the other trader. This effect is shown to drive a form of unraveling; as a result in every equilibrium to the larger game the good ends up in the hands of the agent with the higher valuation.