5. (22 points=5+5+6+6) It is the year 2050, and the NDL (National Dodgeball League) runs the most popular spectator sport in the country. Alice and Bob represent the players' union and ownership respectively, and will negotiate over the surplus of $1 billion (represented as 1 unit.) The negotiations will follow a Rubinstein bargaining model, with no fixed conclusion. Alice has a discount rate of a and Bob of b. For the moment, a and b are known to both players. The standard prediction in this game is that the players agree immediately, with a split of b b(1 - a) ab' 1-ab if Alice offers first and (a(1-b) 1-a) if Bob offers first. = (a) If a = .99 and b .9, who gets more surplus? The answer does not depend on who goes first. Explain briefly the intuition for why this player does better. You do not need to do the arithmetic to calculate the exact amounts; in fact, you should be able to get the answer without the formulas at all, but use them if you like. (b) If a = b = .5 and Alice goes first, what is the exact outcome? If a = b = .99 and Alice goes first, what is the approximate outcome? Explain the intuition for the distinction between your two answers. Math note: (.99) .98. (c) Suppose Alice offers first, and she thinks a = .5, b = .8 but actually a = b = .5 (and Bob knows this). If Bob takes any action which is surprising to Alice, she will wake up to the fact that b = .5. What outcome do you predict? b = .5 but actually a = .5, = .8 (d) Suppose Alice offers first, and she thinks a = (and Bob knows this). If Bob takes any action which is surprising to Alice, she will wake up to the fact that b .8. What outcome do you predict? ==