© 2019 Elsevier Inc. An arbitrator is often introduced into bargaining to avoid disagreement. The arbitrator's role is to impose some agreement when negotiators cannot reach an agreement. However, in models with an arbitrator, a fair agreement for negotiators is eliminated from equilibrium outcomes if the arbitrator is biased. To avoid disagreement without eliminating the achievability of a fair agreement in equilibrium, we consider introducing a mediator. While an arbitrator imposes an agreement, a mediator can only give advice. We analyze a simultaneous-offers bargaining model with a mediator and obtain the following desirable results. First, disagreement is not supported as an outcome of a stationary subgame perfect equilibrium (SSPE). Second, even if a mediator is biased, the fair agreement in the sense of the Nash bargaining solution (NBS) is always one of the SSPE agreements. Finally, if a mediator is fair, negotiators always reach an agreement with the NBS in SSPE.