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

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

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

Part c: Write down an alternative modification of the aboveextensive form (again without modifying any of the decision nodesor branches of the game tree) that introduces new information setsfor which the extensive form game is a game of perfect recall, butof imperfect information. Explain your answer