Amy knows that when she runs over and stands quietly by her grandfather's chair, he will reach over and tickle her under her chin. enables amy to behave in this specific way to obtain a specific result.

I believe the answer is: Operant conditioning
In operant conditioning, the behavior of the subject would be controlled/influenced by either reward or punishment.
On the scenario above, amy's behaving the way she does because she's expecting the reward from her grandfather (by tickling her)