## Based on the cardinal payoffs shown in Figure 8.8, write down the preference ordering for (a) the Regime, (b) the moderate Religious Party, and (c) the radical Religious Party over the three possible outcomes.

Problem Set 3

1.(a) Based on the cardinal payoffs shown in Figure 8.8, write down the preference ordering for (a) the Regime, (b) the moderate Religious Party, and (c) the radical Religious Party over the three possible outcomes.

(a) the Regime-Hold elections-Pursue moderate policy-Democratic consolidation

(b) the moderate Religious Party-regime-Hold elections-Religious Party-Pursue moderate policy-Democratic consolidation

(c) the radical Religious Party-regime-Hold elections-Religious Party-Pursue moderate policy-Democratic consolidation

(b) Solve the subgame on the left, where the Religious Party is moderate, as if there were no uncertainty. What is the subgame perfect equilibrium? What is the expected outcome? What are the payoffs that each player receives?

The subgame perfect equilibrium as if there were no uncertainty is (Hold elections; Pursue moderate policy), the expected outcome will be Democratic consolidation. The payoff will be (25, 25).

(c) Solve the subgame on the right, where the Religious Party is radical, as if there were no uncertainty. What is the subgame perfect equilibrium? What is the expected outcome? What are the payoffs that each player receives?

The is subgame perfect equilibrium is (Cancel elections; Pursue radical policy). The expected outcome will be continued dictatorship. The player who chooses to continue dictatorship will receive (20,5) as payoff.

(d)What is the expected payoff for the Regime from “Cancel elections”?

The expected payoff for the Regime from “Cancel elections”

will be 20, and the dictatorship will be continued.

20*p + 20*(1-p) = 20

(e)What is the expected payoff for the Regime from “Hold elections”?

The expected payoff for the Regime from “Hold elections” will be 25*p + 5*(1-p) = 20p +5.

(f) Use the expected payoffs from the two previous questions to calculate the critical probability at which the Regime will choose to hold elections rather than cancel them.

Regime would hold elections if the expected payoff from holding elections is greater than the payoff from canceling elections”, meaning 20p + 5 > 20, thus p > .75

(g) If the Regime believes that the Religious Party is moderate with a probability of 0.75, will it choose to hold elections, will it cancel elections, or will it be indifferent between these two actions? Explain.

When p equals .75, the payoff for Regime from holding elections equals the payoff from canceling elections. So it will be indifferent between them.

(h)If the Regime believes that the Religious Party is moderate with a probability of 0.8, will it choose to hold elections, will it cancel elections, or will it be indifferent between these two actions? Explain.

When p equals .8, the payoff for Regime from holding elections is 20 * 0.8 + 5 = 21, which is greater than the payoff from canceling elections. So it will hold elections.

(i) If the Regime believes that the Religious Party is moderate with a probability of 0.5, will it choose to hold elections, will it cancel elections, or will it be indifferent between these two actions? Explain.

When p equals .5, the payoff for Regime from holding election is 20 * 0.5 + 5 = 15, which is smaller than the payoff from canceling elections. So it will cancel elections.

(j) If you represented a moderate religious party poised to win the elections, would you want the Regime to believe that your party was moderate or radical?

If I represent a moderate religious party poised to win the elections, I would want the Regime to believe that my party is moderate.

(k) If you represented a radical religious party poised to win the elections, would you want the Regime to believe that your party was moderate or radical?

If I represent a radical religious party poised to win the elections, I would lie and want the Regime to believe that my party is moderate.

(l) If you solved the game correctly, you will find that the Regime will hold elections as long as it believes that the Religious Party is moderate with a high enough probability. If there is some uncertainty on the part of the Regime and you are representing a moderate religious party that wants the elections to go ahead, why might it not be enough for you to simply announce to the Regime that your party is a moderate religious party and not a radical one?

The critical probability matters. If the regime is really uncertain about the nature of the party, it may suspect that a radical party is masked as a moderate party to persuade the regime to hold elections. Only when p is larger than .75, and the party announce that its moderate, will the regime hold elections

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