I study ultimatum bargaining with imperfectly observed offers. Imperfectly observed offers must be rejected with positive probability, even when the players’ preferences are common knowledge. Noisier observations imply a greater risk of rejection. In repeated ultimatum bargaining, the responding party can obtain a positive payoff if his signal of the opponent’s offer is also observed by the opponent herself, but not if his signal is private. In alternating-offers bargaining, a player is better off when her own offers are observed more precisely and her opponent’s offers are observed less precisely. Possible applications include international relations, regulation, principal-agency, and product quality provision.

We study how discounting and monitoring jointly determine whether cooperation is possible in repeated games with imperfect (public or private) monitoring. Our main result provides a simple bound on the strength of players' incentives as a function of discounting, monitoring precision, and on‐path payoff variance. We show that the bound is tight in the low‐discounting/low‐monitoring double limit, by establishing a public‐monitoring folk theorem where the discount factor and the monitoring structure can vary simultaneously.