No students show up to class -- what should an instructor do?
At my former institution the rule of thumb was a lecturer waited 15 minutes and if no one turned up then the he/she was free to leave (this was common when the period was devoted to a problems class). However, even if one student out of the class turned up then we were expected to present the lecture. 

The only case where I didn't follow this was one time out of a class of approximately 30 students one solitary student turned up. This was rather extreme so I checked and found that the students were on a field trip that day (I hadn't been informed which was rather bad) and the student who had turned up often missed lectures and had, apparently, missed the lecture when the field trip was discussed.

Because of this, the majority of students had good reason to be away I decided not to take the class since, effectively, the students on the field trip would have been at a disadvantaged through no fault of their own.