1. Consider a dynamic game of complete and perfect information. Suppose there are now simultaneous moves in each stage. How does this change the description of the game? 2. Consider a two-stage game of complete but imperfect information where players 1 and 2 simultaneously choose actions a1 and a2 in stage 1 and players 3 and 4 simultaneously choose actions a3 and a4 in stage 2. Provide the notation for the Nash equilibrium in stage 2. How come players 1 and 2 can anticipate this outcome in stage 2 ? 3. Provide the notation for the subgame perfect outcome of the game described in question 2. Subgame perfection is a combination of what two solution concepts? 4. Two investors have each deposited 5 (all amounts are in $10,000 s) 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 3 and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives 5 , the other receives 1 , 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 7 and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 9 , the other receives 5 , and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns 7 to each investor and the game ends. Show the bi-matrix for dates 1 and 2. 5. Find the subgame perfect outcomes for the game described in question 4. Which of these outcomes is consistent with a "bank run"? 1. Consider a dynamic game of complete and perfect information. Suppose there are now simultaneous moves in each stage. How does this change the description of the game? 2. Consider a two-stage game of complete but imperfect information where players 1 and 2 simultaneously choose actions a1 and a2 in stage 1 and players 3 and 4 simultaneously choose actions a3 and a4 in stage 2. Provide the notation for the Nash equilibrium in stage 2. How come players 1 and 2 can anticipate this outcome in stage 2 ? 3. Provide the notation for the subgame perfect outcome of the game described in question 2. Subgame perfection is a combination of what two solution concepts? 4. Two investors have each deposited 5 (all amounts are in $10,000 s) 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 3 and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives 5 , the other receives 1 , 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 7 and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 9 , the other receives 5 , and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns 7 to each investor and the game ends. Show the bi-matrix for dates 1 and 2. 5. Find the subgame perfect outcomes for the game described in question 4. Which of these outcomes is consistent with a "bank run