Answer Happy

QUESTION (3) Two investors have each deposited 100$ with a bank. The bank has invested these deposits in a long-term project If the bank is forced to liquidate its investment before the project matures, a total of 150$ can be recovered. If the bank allows the project to reach maturity, however, the project will pay out a total of 400$. Consider a two stage-game played by the two investors. Each can choose to withdraw or not at two dates. Date 1 before the bank's investment matures; date 2 is after. In each period, the decision to withdraw or not is made simultaneously. Date 1: If both investors make withdrawals at date 1 then each receives 75$ simultaneously and the game ends. If only one makes a withdrawal at date 1 then that investor receives 100$, the other receives 50$ and the game ends. Finally, if neither investor makes a withdrawal at date 1, the game moves to the second stage. Date 2: At date 2, each investor knows the choice made by both of the investors at date 1. If both withdraw then each receives 200$. If only one investor withdraws, that investor receives 300$ while the other receives 100$. Finally, if neither investor makes a withdrawal at date 2 then the bank returns 200$ to each investor. (a) Form the payoff matrices for both of the dates. (b) Compute all of subgame perfect outcomes.