Final answer:
George used the foot-in-the-door technique on his brother by starting with a large request and then moving to smaller ones until he gained compliance with a $20 request.
Step-by-step explanation:
The persuasion technique used by George on his brother Anthony is known as the foot-in-the-door technique. This technique involves encouraging a person to agree to a small favor, only to later request a larger favor. Initially, George asks for $200, then $50, and finally settles for $20. Anthony's compliance with the smallest request after refusing the larger ones is a classic example of this technique. It works on the principle of consistency, where once someone agrees to a small request, they are more likely to agree to a larger one later on.