There is some popular unrest in a dictatorship. The population might be in a revolutionary mood, in which case they would be willing to violently overthrow the dictator, or just grumbling, in which case they would not. There is a 30% chance the population is in a revolutionary mood. The population knows their own type, but the dictator does not. After nature chooses whether the population is in a revolutionary mood, the population can decide to protest or not. The dictator observes the populations behavior, and then can peacefully resign or hold onto power. The dictator can make this choice whether or not the population protests. If the dictator holds onto power, the population can violently overthrow the dictator or not. The dictator gets 50 utility for retaining power, 0 utility if they peacefully resign, and -100 utility if they are overthrown. The revolutionary population gets 50 utility for the dictator resigning, 30 utility for overthrowing the dictator, and -50 utility for the dictator retaining power. The grumbling population gets 10 utility for the dictator resigning, -10 utility for overthrowing the dictator, and 0 utility for the dictator retaining power. In addition, both population types would pay 15 utility for protesting, which would be subtracted from the above utilities. a. Draw a signaling game to represent this situation b. Is there a separating equilibrium? c. Is there a pooling equilibrium?
There is some popular unrest in a dictatorship. The population might be in a revolutionary mood, in which case they would be willing to violently overthrow the dictator, or just grumbling, in which case they would not. There is a 30% chance the population is in a revolutionary mood. The population knows their own type, but the dictator does not. After nature chooses whether the population is in a revolutionary mood, the population can decide to protest or not. The dictator observes the populations behavior, and then can peacefully resign or hold onto power. The dictator can make this choice whether or not the population protests. If the dictator holds onto power, the population can violently overthrow the dictator or not. The dictator gets 50 utility for retaining power, 0 utility if they peacefully resign, and -100 utility if they are overthrown. The revolutionary population gets 50 utility for the dictator resigning, 30 utility for overthrowing the dictator, and -50 utility for the dictator retaining power. The grumbling population gets 10 utility for the dictator resigning, -10 utility for overthrowing the dictator, and 0 utility for the dictator retaining power. In addition, both population types would pay 15 utility for protesting, which would be subtracted from the above utilities. a. Draw a signaling game to represent this situation b. Is there a separating equilibrium? c. Is there a pooling equilibrium?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:7) There is some popular unrest in a dictatorship. The population might be in a
revolutionary mood, in which case they would be willing to violently overthrow the
dictator, or just grumbling, in which case they would not. There is a 30% chance the
population is in a revolutionary mood. The population knows their own type, but the
dictator does not. After nature chooses whether the population is in a revolutionary
mood, the population can decide to protest or not. The dictator observes the populations
behavior, and then can peacefully resign or hold onto power. The dictator can make this
choice whether or not the population protests. If the dictator holds onto power, the
population can violently overthrow the dictator or not. The dictator gets 50 utility for
retaining power, O utility if they peacefully resign, and -100 utility if they are overthrown.
The revolutionary population gets 50 utility for the dictator resigning, 30 utility for
overthrowing the dictator, and -50 utility for the dictator retaining power. The grumbling
population gets 10 utility for the dictator resigning, -10 utility for overthrowing the
dictator, and 0 utility for the dictator retaining power. In addition, both population types
would pay 15 utility for protesting, which would be subtracted from the above utilities.
a. Draw a signaling game to represent this situation
b. Is there a separating equilibrium?
c. Is there a pooling equilibrium?
d. Now consider the same game, except the population only pays 5 utility for
protesting. Is there a separating equilibrium in the new game? Is there a pooling
equilibrium?
e.
What do your results say about protest?
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