One Sunday afternoon, your mother tells you and your brother that you can quickly make some money by helping her wash dishes. Both of you decide to help her. Once both of you are done with the work, your mother gives you a $20 bill

She also says that you can divide the money between yourself and your brother in any proportion you want, but if your brother does not accept the amount he is being given, she will take all of the money back. a) How much money should you offer your brother if he prefers more money to less? b) How much money should you offer to your brother if you know that your brother prefers fairness to money?

a) You should allot a minimum amount of money to your brother if he prefers more money to less as he would always accept your offer and you will be able to make more money.
b) You should make your decision using the method of backward induction in this case. Because your brother values fairness to money, he will not accept the offer if he does not get an equal share of money. In case he rejects the offer, neither of you will get any money because your mother will take the money back. Therefore, you should divide the money into two equal parts.