Conquerors are invading the same island country, but now the conquerors consider

Question

Conquerors are invading the same island country, but now the conquerors consider the idea of intentionally sinking their own ships upon arrival. The defenders can still either fight (F) or give up (G). Once the defenders decide on what to do, the conquerors can still either stay to take over (S) or leave (L), but they have no boats to leave on. The defenders and conquerors can see what the other party chose to do.

To review, the defenders start with 6 utility points. If they fight and the conquerors leave, or if they give up, but the conquerors still leave, they keep their country and nobody dies (±0). If they give up and the conquerors stay, they lose their country (-2). If the fight and the conquerors stay, they lose their country (-2) and many die (-2).

The conquerors still start with 4 points. If they choose to keep their boats, nothing changes. If they leave, they gain nothing and lose nothing (±0). If the defenders give up and they stay, they gain a country (+2). If the defenders fight and they stay, they gain a country (+2), but many die (-4).

If the conquerors choose to sink their boats, two things change. First, they no longer have their boats, even if they conquer the new country (-1). Second, if they decide to leave, it is a long swim home so nearly everyone dies (-4).

Develop the Extensive Form Game, and using Backward Induction, determine the solution and payoff for each player. Explain your steps. Although not required, you may include a tree diagram if it would help you explain your thought process.

Explanation / Answer

Now from the given

Repeat the same analysis from given

Strategic form: 2

ac ad bc bd

1 D 2 -,2 2,-2 -4,2 -4,2

C 2,1 2,2 2,1 2,2

Now we have three Nash equilibria.However ,player two is now indifferent about pay-off in the subgame

after one plays D.

Lets try backwards induction:

If one plays C ,two certainly plays d,since 4>1

if one plays D, two might play a or b ,there's no way to throw either posibility out.

Then

and

Specify two sub-game perfect equilibria .

In particular,we throw out (D,ac)

because it hinges on player one believing that player twowould use c against C.

You can see this is irrational.

If one plays C,only hurts Defender by using c when d is available,since 4>1.

Again we have used backwards induction and subgame perfection to throw out an unreasonable equilibrium.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.