Introduction to Game Theory Spring 2022 Problem set 3 Due: March It] Be sure to show at? your workfor partial credit. 1. {13 points} Consider the following extensive form game: (3'11 {1.3) [13) (3.1) (a) Give the normal form representation of this game. (b) Find the Nash equilibria. (c) Using Backward Induction. find the Subgame Perfect Nash Equilibrium of this game. 2. (12 points) Consider a game in which players A and B both have two actions, Left and Right. In each case below, once the game has been played, it is repeated for a second time [so both A and B move twice in total). For each case, {i} draw the corresponding game tree with the appropriate information sets; {ii} give the number of strategies each player has: {iii} give the number of subgames of the game. (a) A moves first, B observes A's action, then B moves. A then observes B's action, and the game is repeated in a similar fashion. In what follows, assume that players simultaneously decide between Left and Right, and this simultaneous game is played twice. (b) Once the game has been played for the rst time, players' actions are publicly revealed. Players then play again, to) l[Since the game has been played for the first time, player B learns the action A has taken. Player A learns nothing. Players then play again