Optimal Dynamic Mediation

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.