Question

Two countries, A and B, are at war. A small island sits between A and B, but is closer to A. Each country only has one bridge that can access the island. Although valuable, the island is not worth fighting over; each side would rather concede the island to its opponent than fight a battle over it. Since the island is closer to A, A will get to the island first and has to decide whether to burn down the bridge. Burning down the bridge would send a strong signal that they will fight for the island because there is no way to go back on land. B then decides whether to invade the island.

• If A has burnt the bridge and B invades, then they must fight for the island as A cannot go back on land. In this case, both A and B will get utilities of -1

• If A has not burnt down the bridge and B decides to invade, A then has two options, to retreat and go back on land OR to fight.

  o If A retreats, then B get the island without having to fight and therefore B will get 1, and A will get 0

  o If A decides to fight, both will get utilities of -1

• If B does not invade the island, no matter if A has burnt down the

  bridge or not, A will get 1 and B will get 0 for utilities

1.1) Please write down this game in an extensive form

1.2) What is the backward induction solution to this game

Answer 1