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 ofthe game. (a) A moves rst, 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. (c) Once the game has been played for the rst time, player B learns the action A has taken. Player A learns nothing. Players then play again. (d) Once the game has been played for the rst time, player A learns the action B has taken. Not only docs player B not learn anything, but he forgets what action he chose. Players then play again