It makes the most economic sense for both parties to show up late for an appointment. Andrew Chamberlain expalins why in "Puncutality is Inefficient". Basically, waiting is costly. In an opportunity cost sort of way. You don't want to wait because it costs you, and so does coming early. As a result, each party assumes that the other person will be late, and therefore to avoid cost, each arrives late.
Chamberlain has a little analogy set up to help expalin this phenomenon. Thank goodness for what he calls "social costs", which are costs that will be incured if one shows up too late. An example of a social cost is the unwillingness of the other party to deal with you in the future. If not for these costs we would all keep second guessing the model. We would assume that the other person is assuming that we will be late, and that they will show up lateras a result. We would then think it was alright for us to show up even later. If this kept going on, nobody would ever show up.
This is a cool way to think about why people are late. But it could be dangerous if misused. Sometimes the opportunity cost of being late is overcome by the benefit of being on time, or early. Employing Chamberlain's theory when going to a job interview could prove to be disasterous. So while the theory may be interesting, it is not necessarily always correct.