A buyer and seller bargain in continuous time over a good. Bargainers can be rational or committed to some fixed price. A rational buyer has a private value and outside option. If the set of buyer values and commitment types is rich and the probability of commitment vanishes, outcomes are partially consistent with the Coase conjecture: the seller chooses a price below the maximum of the lowest outside option and half the lowest value; the buyer immediately accepts or takes his outside option.

I highlight how reputational concerns provide a natural explanation for “deadline effects, ” the high frequency of deals prior to a deadline in bargaining. Rational agents imitate the demands of obstinate behavioral types and engage in brinkmanship in the face of uncertainty about the deadline's arrival. I also identify how surplus is divided when the prior probability of behavioral types is vanishingly small. If behavioral types are committed to fixed demands, outcomes converge to the Nash bargaining solution regardless of agents' respective impatience. If behavioral types can adopt more complex demand strategies, outcomes converge to the solution of an alternating offers game without behavioral types for the deadline environment.

Can an uninformed mediator improve outcomes in a dynamic reputational bargaining model? I show that a simple communication protocol used by professional mediators, of announcing an agreement only if both parties privately accept its terms, can increase the payoffs of rational bargainers, but only if communication is noisy: the mediator must sometimes fail to suggest a deal even when both bargainers accept it. (JEL C78, D74, D83)

How should mediators communicate with bargainers? When can they improve outcomes? Can arbitrators that impose outcomes do better? I provide answers in wars of attrition with flexible and commitment types, consistent with reputational bargaining. I characterize the unique mediated equilibrium, which maximizes flexible types’ payoffs. The mediator immediately elicits private information but waits to suggest agreements. She front-loads agreements between flexible types, while initially delaying any involving commitment types. This improves on unmediated outcomes only if commitment probabilities are less than agents’ payoff share in their preferred agreement. Arbitrators do strictly better but sometimes impose disagreement, which may be hard to enforce.

We study bargaining over contingent contracts in problems where private information becomes public or verifiable when the time comes to implement the agreement. We suggest a simple, two-stage game that incorporates important aspects of bargaining. We characterize equilibria in which parties always reach agreement, and study their limits as bargaining frictions vanish. Under mild regularity conditions, we show all interim-efficient limits belong to Myerson’s (1984) axiomatic solution. Furthermore, all limits must be interim efficient if equilibrium beliefs satisfy no-signaling-what-you-don’ t-know. Results extend to other bargaining protocols. (JEL C78, D82, D83, D86)