Player 1 first makes a decision of choosing between 1 or 0. Then player 2 observes this action and then chooses between 1 or 0. Player 1 moves again and chooses between A or B, having observed all previous decisions. Finally, player 2 observes all previous choices by all players and chooses between A or B. You can make up whatever payoffs you want as it will not affect the rest of the problem.

Part a: Write the extensive form of the above game. Is this a game of perfect information?

Part b: Write down a modification of the above extensive form game (without modifying any of the decision nodes or branches of the game tree) that introduces new information sets for which the extensive form game represents a game of imperfect recall.

Part c: Write down an alternative modification of the above extensive form (again without modifying any of the decision nodes or branches of the game tree) that introduces new information sets for which the extensive form game is a game of perfect recall, but of imperfect information.