A certain game Gn works as follows: n dice are rolled, and you receive a payoff equal to 100 times the highest number on any dice (so, for example, if n = 3 and you roll {2, 5, 5}, you receive $500)

(a) Calculate the payoff distribution for G1 (i.e., if n=1, one die is rolled) and the payoff distribution for G2 (i.e., if n=2, two dice are rolled).

(b) Now assume that players have to pay for the right to play the game. Let Wn be the price that makes a player indifferent between not playing the game, and paying Wn to play Gn. Your friend Josh is risk-neutral. Calculate w1 and w2 for him.

(c) Your friend Sarah tells you that, for her, w1 = 270. You know that Sarah's utility, as a function of her net payoff, is increasing and concave, but you don't know her specific utility function. What can you say about w2? Explain your answer. (Note: Clearly, you cannot find her exact w2, so we are looking for statements of the form "It must be true that w2 is between ...and ..., because ...")