There is no requirement that the parties give each other their briefs. The process is what disputants and lawyers make of it. Flexible, it bends to imaginative sculpting. Sometimes mediations do not immediately end in resolutions. The advocate ought not to give up.
Good mediators continue to keep trying to assist the disputants to reach a resolution.
The mediation can be the stage for displaying the hurt, credibility, charm and jury appeal of the client. And the clients can talk directly to one another across the table. But so are first night jitters. This is time well spent. Timing, rhythm and pace are all important in mediation.