Three friends, A, B. and C, are preparing a group project for their research class. Due to their class schedule. they can't work together. A moves rst, B moves second, and C moves last and turn in the project as it is. Each of there has ve options, working or shirking. If only one of them or no one works on the project, they will get an F and payoff of that score equals -$l. If two of them work on the project, they will get a E and payoff of that score equals 51. If they all work on the project, they will get an A and payoff of that score equals 3] .5. In addition to the payoff from score, the playeris} choose to shirk get additional payoff equals S]. For example, ifA and E Work on the project and C shirk, then A gets $1, E gets $1, and C gets $I+$l=$2. a. Draw the game tree for this three-person sequential game. It. How many strategies each player has? c. 1What is the rollback equilibrium of this game? d. Does this game have a rst-mover advantage? Why or why not? e. Now suppose the game become simultaneous game. Three friends each chooses to work or shirk simultaneously. The payoffs are the same as described in the question. Draw the game table for this game. E What are the Nash equilibria in pure strategies for the game in part e. List out all of theta