Military Intervention Game
In the strategic game shown in Figure 1, below, the military in some unidentified country is split between those who wish to intervene in the political system and launch a coup (overthrowing the civilian government) and those who wish to maintain their apolitical position as members of the armed forces. Both military factions prefer that the military act as a cohesive unit, however.
Figure 1: Normal Form Military Intervention Game
A similar situation between two military factions is shown in the extensive form game shown below. The key difference with the earlier game is that the faction that wishes to take over the civilian government makes the first move.
Figure 2: Extensive Form Military Intervention Game

-What is the subgame perfect Nash equilibrium?

Question

Military Intervention Game
In the strategic game shown in Figure 1, below, the military in some unidentified country is split between those who wish to intervene in the political system and launch a coup (overthrowing the civilian government) and those who wish to maintain their apolitical position as members of the armed forces. Both military factions prefer that the military act as a cohesive unit, however.
Figure 1: Normal Form Military Intervention Game
  A similar situation between two military factions is shown in the extensive form game shown below. The key difference with the earlier game is that the faction that wishes to take over the civilian government makes the first move.
Figure 2: Extensive Form Military Intervention Game
 
-What is the subgame perfect Nash equilibrium?

Quizplus · Accepted Answer

In the subgame starting from the first decision node, the faction that wishes to launch a coup will make the first move, as shown in Figure 2. The other faction can then choose to either stay out or launch a coup as well. In this subgame, the Nash equilibrium is for both factions to launch a coup. This is because if the first faction launches a coup and the second faction stays out, the military will not act as a cohesive unit, which is what both factions prefer. Therefore, the second faction has an incentive to also launch a coup. This results in the outcome (Launch coup, Launch coup) in the subgame, which is also the overall subgame perfect Nash equilibrium. The other options (A, B, and D) do not result in a Nash equilibrium.

Military Intervention Game in the Strategic Game Shown in Figure 1, Below, the 1