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. Part I. Suppose the people first choose to revolt or not. Then the leader observes this choice and decides to democratize or not. A. Write down the game. B. Find the subgame-perfect equilibria of this game, by using backward induction. C. Does this game exhibit a commitment problem? Explain.
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.
Part I. Suppose the people first choose to revolt or not. Then the leader observes this choice and
decides to democratize or not.
A. Write down the game.
B. Find the subgame-perfect equilibria of this game, by using backward induction.
C. Does this game exhibit a commitment problem? Explain.
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