Joe, Rob, and Andy are treasure hunters. They find 1000 gold coins.

Rob has first choice from the three bags of coins. Andy then gets to choose from the remaining two bags, before Joe receives the final bag.

The two potential divisions of the gold coins are as follows:

(i) 250, 350, 400

(ii) 200, 300, 500

Each person's payoff is the number of coins that he gets.

(a)Using backward induction, briefly describe the outcome of this game under both scenarios. Who will receive which bag of coins?

b) If Joe could choose how to divide the coins into three bags, what division would he choose? (He still receives the last bag of coins, with Rob and Andy choosing before him.)