Problem 6. Alice and Bob play the following game. Alice has 100 chips. First, she publicly distributes the chips between two boxes. Then she shuffles the boxes and offers Bob to buy one of them. Without knowing how many chips are in the box he is offered, Bob makes take-it-or- leave-it offer of the price. Alice knows what is inside the box for sale, and if she accepts the offer, they trade, if not, then the game is over and no trade occurs. Alice values chips at $1 each, whereas Bob values them at $1.5 per chip. Both maximize the expected amount of money they are left with. Note, that Alice always keeps one of the boxes to herself, and that Bob knows the initial distribution of chips between the boxes, but does not know how many chips are in the box for sale. As usual, you may assume that if someone is indifferent between several actions, then they will choose an action that benefits the other party. 1. Suppose Alice puts 0 chips in one box and 100 in the other. Bob is offered one of these boxes randomly (each being equally likely), and Alice knows which box he is offered. What is the best price for Bob to offer? 3 2. What is the optimal way to distribute chips between the boxes for Alice?