I'm not sure I understand why Greg Mankiw thinks economists "don't understand tipping." When I was learning economics, I learned that people are utility-maximers and that whenever you see some behavior that doesn't seem explicable in purely financial terms that must be because people are deriving utility from the foregone financial advantage. Thus, as any economist could tell you, people tip because of the utility they derive from the tipping in much the way that economists can explain all aspects of human life.
Have I ever mentioned that philosophers tend to think that economics is vacuous? Which isn't to say that you shouldn't listen to economists. These days, they tend to know a lot of math, and math is a very useful thing.