Two players, A and B, take part in a sequential-move game. A moves first, B moves second, and each player moves only once. A has two possible actions: Left or Right. No matter what A chooses, B has three possible actions: Top, Middle, or Bottom. The payoffs for the two players are summarized as follows:
Case 1: A chooses Left and B chooses Top; A’s payoff is 3; B’s payoff is 2.
Case 2: A chooses Left and B chooses Middle; A’s payoff is 4; B’s payoff is 1.
Case 3: A chooses Left and B chooses Bottom; A’s payoff is 2; B’s payoff is 3.
Case 4: A chooses Right and B chooses Top; A’s payoff is 2; B’s payoff is 1.
Case 5: A chooses Right and B chooses Middle; A’s payoff is 1; B’s payoff is 4.
Case 6: A chooses Right and B chooses Bottom; A’s payoff is 4; B’s payoff is 3.
(a) Draw a game tree to illustrate this game. Please label all the nodes and branches carefully.
(b) List all the strategies player A has; list all the strategies player B has.
(c) Find the rollback equilibrium for this game.