Twice recently, I attended mediations where I ultimately learned that the opposing lawyer failed to bring a client with him who had authority to settle the case. On one, my client was fortunate to learn that disturbing fact fairly quickly; we walked out of the mediation after only wasting about two hours (not including travel time). On the second, we were not so fortunate. We did not learn that our adversary failed to have someone present with settlement authority until approximately 5:30 p.m. - eight hours after we began the mediation. The client, in essence, paid three lawyers for accomplishing nothing. Additionally, two of their representatives did nothing at work that day. In hindsight, there really isn't much we could have done to avoid this.
Relying on your adversary being truthful, which we did in both of these cases, unfortunately, sometimes is not enough. What I will do with these parties in the future is refuse to mediate with them, unless they represent to the mediator in writing that their client representative will be physically present and will have actual settlement authority. Requiring them to pay exclusively for the second round, if such occurs, is something to be considered, but probably would not be well received.