2. Consider the payoff matrix below: Player 1 Strategy B Strategy A b) Player 2 Strategy A Strategy B (2,2) (5,0) (0,5) (3,3) a) What is Player 1's dominant strategy (if they have one)? What is Player 2's dominant strategy (if they have one)? Does this game have a Nash Equilibrium? If so, what is/are they?

a) Consider the following game matrix: 7 6. 9 - 4 -3 6. 10 A = 3 4 2 10 - 2 i) Determine the optimal mixed strategies. ii) Does the game have a saddle point? If so, give the value of the game and interpret it 6 ㅇ5

5. For each of the following game matrices, determine whether there is a saddle point. Copy the game matrix and circle all saddle points of the matrix if there are any. (a) (b) (c) -1 -4 5 -3 2 54 ÁNO do -3 7 -3 -4 -1 4 6 -2 2 3 -1 0 -1 3 4 25 2 -2 3 2 4 -20 O 18 0 -3 4 1 2 1 -1 -20 21

Instructions: Show all your work (including bi-matrix and/or game tree when relevant). 1. Two investors have each deposited 4 (all amounts are in $10,000s) with a bank. The bank has invested these deposits in a long-term project. If both investors make withdrawals at date 1 then each receives 2 and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives 4, the other receives 0, and the game ends. Finally, if neither investor makes a withdrawal at date 1 then the project matures and the investors make withdrawal decisions at date 2. If both investors make withdrawals at date 2 then each receives 8 and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 10, the other receives 6, and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns 8 to each investor and the game ends. Find the subgame-perfect outcomes.