Policy makers in Washington, D.C., face a dilemma. On the one hand they can try to
pressure the Iraqi government into trying to disarm the militias. If the effort to disarm the
militias succeeds, this might put an end to the sectarian violence and bring some sort of
stability to Iraq. If the efforts fail, there will be even more violence and a still more
gruesome civil war. How likely any attempt to disarm the militias is to succeed depends on
the strength of the Iraqi government. The stronger it is, the more likely these efforts are to
succeed.
In the game below, the US decides how much pressure (p) to exert on the Iraqi
government (e.g., threatening to set a fixed timetable for withdrawing American troops).
The Iraqi government then decides whether to attempt to disarm the militias or not. If the
government does try to disarm the militias, then these efforts succeed with probability δ.
The stronger the government, the higher the value of δ and the more likely the government
is to be able to disarm the militias and avoid a full-scale civil war.
/ Civil War = -100,-100
/1-delta
N
\ delta
\ militias disarmed = 50,50
100 attempt to disarm
/ /
US P.......
\ \
0 Not disarm -20-p, 80-p
QUESTION
If delta = .8, what is the subgame perfect equilibrium of this game? (Assume that Iraq accepts
and attempts to disarm if it is indifferent between attempting to disarm and not.)
To find the subgame perfect equilibrium of this game, we need to analyze the possible strategies and outcomes for each player based on their decision-making process.
In this game, there are two players: the US and the Iraqi government. The US decides how much pressure (p) to exert on the Iraqi government, and the Iraqi government decides whether to attempt to disarm the militias or not. The outcome is determined by the strength of the Iraqi government (represented by delta) and the decisions made by both players.
To determine the subgame perfect equilibrium, we need to consider the possible strategies and outcomes at each decision point and analyze the payoffs for each player.
First, let's consider the Iraqi government's decision to disarm or not. Given delta = 0.8, if the government decides to disarm, there is a 0.8 probability that the disarmament efforts succeed, resulting in a payoff of 50 for both players. On the other hand, if the government decides not to disarm, there is a 0.2 probability of a civil war, resulting in a payoff of -100 for both players.
Next, let's consider the US's decision on how much pressure (p) to exert on the Iraqi government. The US wants to maximize its own payoff while taking into account the potential outcomes based on the Iraqi government's decision.
If the US exerts a high level of pressure (p), it increases the likelihood that the Iraqi government will decide to disarm. However, the US also incurs a cost depending on the level of pressure exerted. In this game, the cost is (20 + p) if the Iraqi government decides not to disarm, and (80 + p) if the disarmament efforts fail.
To find the subgame perfect equilibrium, we need to identify the strategies that maximize each player's payoff given the strategies of the other player.
Based on the information provided, the subgame perfect equilibrium can be determined as follows:
1. If the Iraqi government decides to disarm, the US's optimal strategy is to exert the highest possible level of pressure (p = 100), as this maximizes its payoff of 50.
2. If the Iraqi government decides not to disarm, the US's optimal strategy is to exert the lowest possible level of pressure (p = 0), as this minimizes the cost incurred.
Considering these optimal strategies, the subgame perfect equilibrium of this game is for the US to exert a high level of pressure (p = 100), and the Iraqi government to decide to disarm.