One-sided Uncertainty and Delay in Reputational Bargaining

A two-person infinite-horizon bargaining model where one of the players may have either of two discount factors, has a multiplicity of perfect Bayesian equilibria. Introducing the slightest possibility that either player may be one of a rich variety of stationary behavioral types singles out a particular solution and appears to support some axiomatic treatments in the early literature in their conclusion that there is a negligible delay to agreement. Perturbing the model with a slightly broader class of behavioral types that allows the informed player to delay making his initial demand still achieves powerful equilibrium refinement. But there is substantial delay to agreement, and predictions depend continuously on the ex ante probabilities of the patient and impatient types of the informed player, counter to what the literature suggests. This research was supported in part by National Science Foundation Awards 0922125 and 0922167. We are grateful to Deepal Basak, Martin Osborne and several anonymous referees for providing valuable comments. Thanks also to Juan Dubra and Phil Reny for helpful discussions.