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.

Assume the parameters in part a except that B’s costs of war are only 0.5. (Country’s A’s costs of war are still 0.15 and its probability of winning the war is 0.50). What is A’s expected utility of war? What is B’s expected utility of war? 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? What is the bargaining range? Who is in the better bargaining position? Why?

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 is 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.

A's probability of winning the war is 0.50.

Assuming that ties cannot occur, B's probability of winning the war is 1 - 0.50 = 0.5

B’s costs of war = 0.5

A’s costs of war = 0.15

A’s expected utility of war = 0.5*1 + 0.5*0 - 0.15 = 0.35

B’s expected utility of war = 0.5*1 + 0.5*0 - 0.5 = 0

To avoid war, A has to receive utility . This happens when border point .

Therefore, the range of bargains that A would accept to avoid war is .

To avoid war, A has to receive utility . This happens when border point .

Therefore, the range of bargains that B would accept in order to avoid war is  .

The bargaining range is given by the intersection of the ranges that A and B accept i.e.

A is in the better bargaining position as the B will avoid war even if A captures all of the territory i.e. x=1.