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3. (Infinitely Repeated Game). Two banks are competing for loans from clients. They compete through charging different interest rates (e.g. 4%, 6%, and 8%). The amount of loans (in million pesos) that each bank secures and the combination of interest rates are shown in the payoff matrix below Bank 2 4% 6% 8% Bank 1 4% 0,0 2, 1 4, -1 6% 1,2 4,4 7,1 8% -1,4 1,7 5,5 a. What is the pure strategy Nash equilibrium if this game is played once? b. Can cooperation (i.e. both banks charging 8% and earning 5 million pesos each) be sustained as a subgame perfect nash equilibria (SGPNE) through the following trigger strategy? or not At t=1: Cooperate by charging 8% In period t>1: Charge 8% if both banks charged 8% in the previous period, charge 6% forever if one or both banks in all previous periods did charge 8% c. Consider now the following strategy (Temporary punishment in the Trigger Strategy): period, At t=1: Cooperate by charging 8% In period t>1: Charge 8% as long as both banks charge 8% in the previous period. If one of the banks did not charge 8% in the previous charge 6% for three periods then return to 8% afterwards.

3. (Infinitely Repeated Game). Two banks are competing for loans from clients. They compete through charging different interest rates (e.g. 4%, 6%, and 8%). The amount of loans (in million pesos) that each bank secures and the combination of interest rates are shown in the payoff matrix below Bank 2 4% 6% 8% Bank 1 4% 0,0 2, 1 4, -1 6% 1,2 4,4 7,1 8% -1,4 1,7 5,5 a. What is the pure strategy Nash equilibrium if this game is played once? b. Can cooperation (i.e. both banks charging 8% and earning 5 million pesos each) be sustained as a subgame perfect nash equilibria (SGPNE) through the following trigger strategy? or not At t=1: Cooperate by charging 8% In period t>1: Charge 8% if both banks charged 8% in the previous period, charge 6% forever if one or both banks in all previous periods did charge 8% c. Consider now the following strategy (Temporary punishment in the Trigger Strategy): period, At t=1: Cooperate by charging 8% In period t>1: Charge 8% as long as both banks charge 8% in the previous period. If one of the banks did not charge 8% in the previous charge 6% for three periods then return to 8% afterwards.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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3. (Infinitely Repeated Game). Two banks are competing for loans from clients. They compete through charging different interest rates (e.g. 4%, 6%, and 8%). The amount of loans (in million pesos) that each bank secures and the combination of interest rates are shown in the payoff matrix below Bank 2 4% 6% 8% Bank 1 4% 0,0 2, 1 4, -1 6% 1,2 4,4 7,1 8% -1,4 1,7 5,5 a. What is the pure strategy Nash equilibrium if this game is played once? b. Can cooperation (i.e. both banks charging 8% and earning 5 million pesos each) be sustained as a subgame perfect nash equilibria (SGPNE) through the following trigger strategy? or not At t=1: Cooperate by charging 8% In period t>1: Charge 8% if both banks charged 8% in the previous period, charge 6% forever if one or both banks in all previous periods did charge 8% c. Consider now the following strategy (Temporary punishment in the Trigger Strategy): period, At t=1: Cooperate by charging 8% In period t>1: Charge 8% as long as both banks charge 8% in the previous period. If one of the banks did not charge 8% in the previous charge 6% for three periods then return to 8% afterwards.
Transcribed Image Text:3. (Infinitely Repeated Game). Two banks are competing for loans from clients. They compete through charging different interest rates (e.g. 4%, 6%, and 8%). The amount of loans (in million pesos) that each bank secures and the combination of interest rates are shown in the payoff matrix below Bank 2 4% 6% 8% Bank 1 4% 0,0 2, 1 4, -1 6% 1,2 4,4 7,1 8% -1,4 1,7 5,5 a. What is the pure strategy Nash equilibrium if this game is played once? b. Can cooperation (i.e. both banks charging 8% and earning 5 million pesos each) be sustained as a subgame perfect nash equilibria (SGPNE) through the following trigger strategy? or not At t=1: Cooperate by charging 8% In period t>1: Charge 8% if both banks charged 8% in the previous period, charge 6% forever if one or both banks in all previous periods did charge 8% c. Consider now the following strategy (Temporary punishment in the Trigger Strategy): period, At t=1: Cooperate by charging 8% In period t>1: Charge 8% as long as both banks charge 8% in the previous period. If one of the banks did not charge 8% in the previous charge 6% for three periods then return to 8% afterwards.
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