I'm wondering why airlines don't give an incentive for passengers who know they won't make a flight to inform the airline that they won't be flying.

Surely it would make sense for an airline to offer an incentive to people who know they won't be flying to actually cancel so that the airline will have a better idea of how many no-shows there will be. Surely if the airline had a better idea of how many people won't be flying, there would be less uncertainty involved in overselling so that when passengers cancel, the airline will be able to sell more tickets (perhaps at a lower price more likely to sell - adjusting for the decreased uncertainty), and in cases where no one cancels, the airline will know to oversell fewer tickets (or to sell at a higher price reflective of the increased likelihood of having to compensate).

Any ideas why airlines don't do this?

Am I missing something about overselling or something else?