Economic - Game Theory

1. 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 first, B moves second, and C moves last and turn in the project as it is. Each of them has two 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 -$1. If two of them work on the project, they will get a B and payoff of that score equals $1. If they all work on the project, they will get an A and payoff of that score equals $1.5. In addition to the payoff from score, the player(s) choose to shirk get additional payoff equals $1. For example, if A and B work on the project and C shirk, then A gets $1, B gets $1, and C gets $1+$1=$2. a. Draw the game tree for this three-person sequential game. (7pt) b. How many strategies each player has? (7pt) c. What is the rollback equilibrium of this game? (7pt) d. Does this game have a first-mover advantage? Why or why not? (7pt) 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. (7pt) f. What are the Nash equilibria in pure strategies for the game in part e. List out all of them. (5pt)