two-player game proceeds as follows: A pot of money is created with 27 in it initially. Player 1 moves first, then player 2, then player 1 again, and finally player 2 again. At each players turn to move, he has two possible actions: to be grasping (G for Player 1, g for Player 2) or reasonable (R for Player 1, r for Player 2). If he is grasping he gets 3/4 of the current pot of money, the other player gets 1/4 of the pot, and the game ends. If he is reasonable then the size of the current pot is multiplied by 4/3 and the next player gets to move. At the last stage at which player 2 moves, if he chooses to be reasonable (r) then the pot is still multiplied by 4/3, player 2 gets 1/4 of the pot, and player 1 gets 3/4 of the pot.

a) Model this as an extensive-form game tree, showing actions of players and their payoffs.

b) Is this a game of perfect or imperfect information? How many terminal nodes does the game have? How many information sets?

c) What pure strategies does each player have? How many are they?

d) Find the pure-strategy Nash equilibria of this game. How many outcomes can be supported in equilibrium? (Hint: here it is easier to use the normal form of the game.)