Question 1: The old man has passed away leaving a substantial estate (worth a total of $1,010,000) to his two sons (1,000,000, 10,000) (1,000, 100,000) with a possible endowment to charity as a third beneficiary. Due to an old family feud the brathers (Cain and Abel) are not on speaking terms with each other. As such, the two noncooperative sibling face now an awkward situation in view of their father's will Abel (10,000, 100) that stipulates the following sequence of uneasy decisions. The first move goes to the elder brother (Cain) giving him a choice of taking $100 for himself, giving his younger sibling (Abel) $1, and passing on the remaining balance to charity; or else, relegating the Cain (10, 1,000) decision to Abel. Abel has then the option of taking for himself $1,000, passing on to Cain $10 with the remainder as before going to charity or, yet again, rerelegating the decision back to Cain who can now take for himself $10,000, leaving Abel only $100, ... Abel (100, 1) and so on. With the decision alternating between the two brothers until the entire bequest is exhausted, the situation can be described by a sequential move game tree as depicted to the right. Cain (a) Analyze the game using backward induction. (b) What is the final distribution of the inheritance among the three recipients (Cain, Abel, and Charity)? If your answer isn't consistent with the backward induction analysis, explain your reasoning