Suppose c1 = 0.1, c2 = 0.3, c2 = 0.1, p = 0.5, β = 0.1, and w = 0.6. That is, the cost of going to war for the Challenger is 0.1 (c1 = 0.1), the cost of going to war for the Defender if the Defender is weak is 0.3 (c2 = 0.3), the cost of going to war if the Defender is strong is 0.1 (c2 = 0.1), the probability that the Challenger defeats the Defender in a war is 0.5 (p = 0.5), the benefit of continuing trade is 0.1 for both actors (β = 0.1), and the Challenger believes the Defender is weak with probability 0.6 (w = 0.6).
a) What does the Challenger demand, that is, what is the value of π, if she wants to ensure that the Defender concedes regardless of whether they are weak or strong? Call this the modest demand.
b) What does the Challenger demand, π, if she is willing to make a demand to which the Defender will concede if they are weak, but will reject if they are strong? Call this the bold demand.
c) Does the Challenger prefer to make a modest or bold demand?
d) What is the largest value of w for which the Challenger prefers to make the modest demand?
2. Assume that the values in question 1 are the same, except set β = 0.2. Answer parts a) through d) again.
3. Assume that the values in question 1 are the same, except set β = 0. Answer parts a) through d) again.
4. What do your answers in questions 1 through 3 tell you about the effect of economic interdependence on the likelihood of war.