Imagine a two player game that proceeds as follows.
A pot of money is created with $6 in it initially. Player 1 (Alice) moves first, then player 2 (Bob), then player 1 again and finally player 2 again. At each player’s turn to move, he or she has two possible actions: grab (G) or share (S). If the player grabs, s/he gets 2/3 of the current pot of money, the other player gets 1/3 of the pot and the game ends. If s/he shares then the size of the current pot is multiplied by 3/2 and the next player gets to move. At the last stage in which Bob moves, if he chooses to share then the pot is still multiplied by 3/2 , and Bob gets 1/3 of the pot and Alice gets 2/3 of the pot. a. Model this as an extensive‐form game and draw the game tree. Is it a game of perfect or imperfect information?b. How many terminal nodes does the game tree have? How many information sets are there? What about the number of subgames?c. Please use backward induction to find the subgame‐perfect Nash equilibrium.