Three cities are competing for the winter crops. Winterfell may suggest the following two different divisions: 1) half of all the crops are given to Winterfell, and the other half is split evenly between Valyria and Meereen or 2) each city (Winterfell, Valyria and Meereen) gets an equal share of 1/3 each. Once learning the offer, Valyria and Meereen simultaneously and independently decide whether to accept (A) or deny (D) the division of the crops suggested by Winterfell. If both accept then each city gets the suggested share. Otherwise the cities go to war and each ends up with zero.

a) what is the extensive form for this game

b) Identify all of the subgames and find the subgame perfect equilibria. Explain.

c) Now assume that Winterfell announces one of the two divisions first, then Valyria announces whether he accepts or denies, and finally Meereen chooses to accept or deny, and each city knows the previous announcement(s). what is tthe extensive for this game and find its subgame perfect equilibria. Explain.

d) What are the available strategies for each city in each of the above two scenarios?