Consider a sequential game with two players: Player 1, who plays first, and Player 2, who plays second. Player 1 has three strategies: 1a, 1b, and 1c. Player 1 can also decide not to play, in which case the status quo prevails. On the other hand, Player 2 has two strategies: 2a and 2b. The payoffs for each combination of strategies are presented next: If Player 1 plays strategy 1a and Player 2 responds with strategy 2a, then the payoffs are 0 for Player 1 and 0 for Player 2, i.e., payoffs(1a, 2a) = (0, 0). Following this notation, all other payoffs are: payoffs(1a, 2b) = (1, 1), payoffs(1b, 2a) = (2, 4), payoffs(1b, 2b) = (3, 0), payoffs(1c, 2a) = (4, 0), payoffs(1c, 2b) = (0, 2), payoffs(Status quo prevails) = (1, 0).

a. What is the rollback equilibrium for this game?

b. Draw a tree and clearly show the answer on your response sheet.

c. why did you choose your answer