Alternating-Offer Bargaining with Two-Sided Incomplete Information.

The author studies alternating-offer bargaining games with two-sided incomplete information about the players' discount rates. For both perfect Bayesian equilibrium and a rationalizability-style notion, he characterizes the set of expected payoffs which may arise in the game. The author also constructs bounds on agreements that may be made. The set of expected payoffs is easy to compute and incorporate into applied models. His main result is a full characterization of the set of perfect Bayesian equilibrium payoffs for games in which the distribution over the players' discount rates is of wide support, yet is in a weak sense close to a point mass distribution. The author proves a lopsided convergence result: each player cannot gain from a slight chance that she is a strong type, but the player can suffer greatly if there is a slight chance that she is a weak type. Copyright 1998 by The Review of Economic Studies Limited.