Which Bargaining Solutions are Identified under Unobserved Information Timing?

Abstract

This paper studies identification of bargaining parameters under uncertainty. I show that Nash bargaining weights are not identified in general: for any two interior bargaining weights, there is a pair of games with different information timing under which the weights are observationally equivalent. In contrast, Kalai proportional bargaining admits a moment on expected gains from trade that remains valid whether bargaining occurs ex ante, ex post, or somewhere in between. I show that among bargaining solutions that satisfy independence of irrelevant alternatives, only Kalai proportional bargaining is identified in general: I show identification implies the social choice property of concavity, and I extend Myerson (1981)’s results to rule out other families. I apply these results to multiperiod contracting in transferable utility games, where Nash and Kalai coincide and my analysis can focus on the role of unobserved information on aggregate gains. I show that bargaining weights may be unidentified with multiperiod contracts, but identification can be restored under plausible econometric restrictions.