A Game Theory Question.

Detailed steps are required.

4. [10 points] Censider a centipede game as follows. There are two players 2' = 1,2, and a pile of money associated with each player. Initially, there is one dollar in each pile. Players take turns, with player 1 going rst. On his or her turn, a player plays either \"stop\" or \"continue.\" If player 3' plays \"continue,\" then a dollar is subtracted from i's pile and two dollars are added to j's pile (where i 79 3'). If a player plays \"stop,\" the game ends and each player collects the amount of money in his or her pile. Once each pile contains $6, the game ends automatically. (For example, (1) if player 1 plays \"stop\" immediately, then each player obtains $1; (2) if player 1 rstly plays \"continue\" and player 2 secondly plays \"stop,\" then player 1 obtains nothing and player 2 obtains $3; (3) if player 1 rstly plays \"continue,\" player 2 secondly plays \"continue,\" and player 1 thirdly plays \"stOp,\" then each player obtains $2.) (4.1) Draw the extensive form for this game. (4.2) Find all subgame perfect Nash equilibria by backward induction. (4.3) How many pure strategies are for each player in this game? Identify all of the outcomes (i.e., paths of play) that can arise from pure-strategy Nash equilibria. Justify your