Two players bargain over a single indivisible good and a transfer, with one-sided incomplete information about preferences. Both players can offer arbitrary mechanisms to determine the allocation. We show that there is a unique perfect Bayesian equilibrium outcome. In the equilibrium, one of the players proposes a menu that is optimal for the uninformed player among all menus, such that each type of the informed player receives at least her payoff under complete information. The optimal menu can be implemented with at most three allocations. Under a natural assumption on the uninformed player’s beliefs, the optimal menu coincides with the Myerson’s neutral solution to the bargaining problem in this environment.

We consider social learning in a changing world. With changing states, societies can be responsive only if agents regularly act upon fresh information, which significantly limits the value of observational learning. When the state is close to persistent, a consensus whereby most agents choose the same action typically emerges. However, the consensus action is not perfectly correlated with the state, because societies exhibit inertia following state changes. When signals are precise enough, learning is incomplete, even if agents draw large samples of past actions, as actions then become too correlated within samples, thereby reducing informativeness and welfare.