Two investors have each deposited D 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 2r can be recovered, where D > r > D/2. If the bank allows the investment to reach maturity, however, the project will pay out a total of 2R, where R > D. There are two dates at which the investors can make with- drawals from the bank: date 1 is before the bank's investment matures; date 2 is after. For simplicity, assume that there is no discounting. If both investors make withdrawals at date 1 then each receives and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives D, the other receives 2r – D, 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 R and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 2R-D, the other receives D, and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns R to each investor and the game ends.

Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter5: Investment Decisions: Look Ahead And Reason Back
Section: Chapter Questions
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2.2.B Bank Runs
Two investors have each deposited D 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 2r
can be recovered, where D > r > D/2. If the bank allows the
investment to reach maturity, however, the project will pay out a
total of 2R, where R > D.
There are two dates at which the investors can make with-
drawals from the bank: date 1 is before the bank's investment
matures; date 2 is after. For simplicity, assume that there is no
discounting. If both investors make withdrawals at date 1 then
each receives r and the game ends. If only one investor makes
a withdrawal at date 1 then that investor receives D, the other
receives 2r - D, 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 R and the game
ends. If only one investor makes a withdrawal at date 2 then that
investor receives 2R-D, the other receives D, and the game ends.
Finally, neither investor makes a withdrawal at date 2 then the
bank returns R to each investor and the game ends.
Transcribed Image Text:2.2.B Bank Runs Two investors have each deposited D 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 2r can be recovered, where D > r > D/2. If the bank allows the investment to reach maturity, however, the project will pay out a total of 2R, where R > D. There are two dates at which the investors can make with- drawals from the bank: date 1 is before the bank's investment matures; date 2 is after. For simplicity, assume that there is no discounting. If both investors make withdrawals at date 1 then each receives r and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives D, the other receives 2r - D, 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 R and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 2R-D, the other receives D, and the game ends. Finally, neither investor makes a withdrawal at date 2 then the bank returns R to each investor and the game ends.
2.22. Give the extensive- and normal-form representations of the
bank-runs game discussed in Section 2.2.B. What are the pure-
strategy subgame-perfect Nash equilibria?
Transcribed Image Text:2.22. Give the extensive- and normal-form representations of the bank-runs game discussed in Section 2.2.B. What are the pure- strategy subgame-perfect Nash equilibria?
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