Question

1. 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.

A:

1. Assume that the costs of war are 0.15 for each country. Suppose country A has a probability of winning the war of 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? Is there an area of overlap of these two ranges? If so, what is the bargaining range?

Answer 1

Costs of war for each country = 0.15

Country A’s utility function = x

Country B’s utility function = 1-x

Probability of winning the war for country A = 0.50

Assuming that ties are impossible, the probability of winning the war for country B =1 - 0.5 = 0.50

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

Bs expected utility of war = 0.5*1 +0.5*0 - 0.15 = 0.35

The border point associated with utility(x) 0.35 for A is x=0.35

i.e. A will avoid war it gets utility x greater than or equal to 0.35.

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

The border point associated with utility(1-x) 0.35 for A is x=1-0.35 = 0.65

i.e. B will avoid war it gets utility 1- x greater than or equal to 0.35

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

There is an area of overlap between the ranges which is the bargaining range i.e is the bargaining range