People of a non-democratic government would like to change their regime to get rid of non-democratic rulers and replace them by a democracy. Suppose the people’s utility from the non-democratic regime is 0 and their utility from the democratic regime is Dp > 0. However, they may get the democratic regime by revolting. If they revolt, they have to pay a cost of revolution Rp, where Dp > Rp > 0. Note they pay this cost whenever they revolt. The non-democratic leader has (i) a utility of N` if there is both no democratization and no revolution and (ii) a utility of D` if there is democratization and no revolution. Here N` > D` > 0. However, if there is a revolution, the non-democratic leader has a utility of 0 if they insist on no democratization and a utility of D` − C` > 0 if they give into democratization. Suppose the leader can take an action that limits their power in a non-democracy. By taking this action, their utility from no democratization under no revolution falls to N` − K > 0, where N` − K < D`. First, the leader chooses whether or not to limit their power. Then the people choose to revolt or not. Finally the leader observes the choice and decides whether or not to democratize. A. Write down the game. B. Find the subgame-perfect equilibria of this game, by using backward induction. C. Does this game exhibit solve the commitment problem? Explain.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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People of a non-democratic government would like to change their regime to get rid of non-democratic rulers and replace them by a democracy. Suppose the people’s utility from the non-democratic regime is 0 and their utility from the democratic regime is Dp > 0. However, they may get the democratic regime by revolting. If they revolt, they have to pay a cost of revolution Rp, where Dp > Rp > 0. Note they pay this cost whenever they revolt.

The non-democratic leader has (i) a utility of N` if there is both no democratization and no revolution and (ii) a utility of D` if there is democratization and no revolution. Here N` > D` > 0. However, if there is a revolution, the non-democratic leader has a utility of 0 if they insist on no democratization and a utility of D` − C` > 0 if they give into democratization.

Suppose the leader can take an action that limits their power in a non-democracy. By taking this action, their utility from no democratization under no revolution falls to N` − K > 0, where N` − K < D`. First, the leader chooses whether or not to limit their power. Then the people choose to revolt or not. Finally the leader observes the choice and decides whether or not to democratize.

A. Write down the game.
B. Find the subgame-perfect equilibria of this game, by using backward induction.
C. Does this game exhibit solve the commitment problem? Explain.

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