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 that the probability of A winning the war is 0.65. 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, x

i.e.

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.

Probability of A winning the war is 0.65.

Assuming that ties do not occur, probability of B winning the war is 1 - 0.65 = 0.35

Assume that cost of war = 0

A’s expected utility of war = 0.65*1 + 0.35*0 = 0.65

B’s expected utility of war = 0.35*1 + 0.65*0 = 0.35

A avoids war if its utility(x) is greater than or equal to 0.65. This happens when .

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

B avoids war if its utility(1-x) is greater than or equal to 0.35 i.e. This happens when

The intersection is at x = 0.65.

Bargaining range is only one point, x=0.65. Since bargaining set contains only one point, both the parties are at the same bargaining position.