Apologizing can be very hard, especially when your pride is hurt. And sometimes one opts for a fake apology, not really meaning it. But this does not really fool the apologizee, doesn't? Is the latter then unlikely to forgive? Of course, an economist has an answer to this question.
Verena Utikal performs a laboratory experiment wherein the dictator game is manipulated to sometimes keep outcomes out of the control of the dictator, who can send a message. The receiver can then act on outcome and message, but without knowing whether the outcome was a choice of the dictator. Dictators do send different messages depending on what happened, and receivers do detect lying and punish it. If you considering that there is a mental cost in lying, there does not seem to be much of a point in providing fake apologies. Yet people do it. And consider that in this experiment, all players were anonymous and did not see each other. Imagine in the real world, where they know and face each other. The cost of lying and faking must be even higher. Yet it still happens.