The Dictator of Abydos is worried that the population might protest or rebel, as neighboring countries have recently undergone revolution. The population is similarly inspired to consider rebellion. The Dictator must decide whether to go ahead and repress, do nothing, or step down peacefully. The population has three options: do nothing, engage in mass protest, or violently revolt. These choices must be made simultaneously, without observing what the other player chose. The dictator will lose power if they step down peacefully or the population revolts. However, repression would successfully overpower a revolt, allowing the dictator to retain power. The dictator values their position at 50 utility, which they would lose if they lose power. They would also lose an additional 100 utility if they are ousted in a revolt, as they would imprisoned. The population would gain 50 utility if the dictator steps down and 30 utility if the dictator is ousted in a revolt. Repression would cost each side a base of 10 utility. Repressing protests would cost the population an additional 20 utility, while repressing a revolt would cost the population 50 utility. Repressing peaceful protests would cost the dictator an addition 50 utility, and repressing a violent revolt would cost the dictator an extra 10 utility. Draw the game described above in strategic / normal form. Solve the game to find all pure strategy Nash equilibria.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The Dictator of Abydos is worried that the population might protest or rebel, as neighboring countries have recently undergone revolution. The population is similarly inspired to consider rebellion. The Dictator must decide whether to go ahead and repress, do nothing, or step down peacefully. The population has three options: do nothing, engage in mass protest, or violently revolt. These choices must be made simultaneously,
without observing what the other player chose. The dictator will lose power if they step down peacefully or the population revolts. However, repression would successfully overpower a revolt, allowing the dictator to retain power. The dictator values their position at 50 utility, which they would lose if they lose power. They would also lose an additional 100 utility if they are ousted in a revolt, as they would imprisoned. The population would gain 50 utility if the dictator steps down and 30 utility if the dictator is ousted in a revolt. Repression would cost each side a base of 10 utility. Repressing

protests would cost the population an additional 20 utility, while repressing a revolt would cost the population 50 utility. Repressing peaceful protests would cost the dictator an addition 50 utility, and repressing a violent revolt would cost the dictator an extra 10 utility. Draw the game described above in strategic / normal form. Solve the game to find all pure strategy Nash equilibria.

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