Question

Two countries, A and B, have a conflict over a common border. The border can take values from zero to one, inclusive, where x is the percentage of the disputed territory under Country A’s control. Country B’s ideal point for the border is 0. Country A’s ideal point for the border is one. Country A’s utility function is x and Country B’s utility function is 1-x and, where x is the point at which the border is actually set. If the two countries go to war over the border dispute, the winner will set the border at its ideal point.

Now assume each country has private information. A thinks its probability of winning the war is 0.80. But B also thinks its probability of winning the war is 0.80. (Obviously, at least one of them is wrong). The costs of war are 0.15. What is the range of bargains that A would accept to avoid war? What is the range of bargains that B would accept in order to avoid war? Will A and B be able to reach a negotiated settlement? Why or why not?     

Answer 1

x is the point at which the border is actually set

Country B’s ideal point for the border is x = 0

Country A’s ideal point for the border x = 1

Country A’s utility function = x

Country B’s utility function = 1-x  

If the two countries go to war over the border dispute, the winner will set the border at its ideal point.

Each country has private information. A thinks its probability of winning the war is 0.80. But B also thinks its probability of winning the war is 0.80.

Therefore, in its expected utility calculations, A's probability of winning war = 0.8

And also in B's expected utility calculations, B's probability of winning war = 0.8

The costs of war = 0.15

A's expected utility of war = 0.8*1 + 0.2*0 -0.15 = 0.65

B's expected utility of war = 0.8*1 + 0.2*0 -0.15 = 0.65

A avoids war if it can get utility (x) greater than or equal to 0.65. This happens when .

Therefore, A will accept   to avoid war.

B avoids war if it can get utility (1 - x) greater than or equal to 0.65. This happens when

i.e. .

Therefore, A will accept   to avoid war.

There is no intersection between the two ranges. Hence, A and B will never be able to reach a negotiated settlement.