Question

t of disputed territory controls t of disputed territory hat A controls With no threat, show the range of outcomes that could make both A and B better off. 9. Looking at the previous question, suppose A has a probability of defeating B equal to 0.80 (so B's probability of defeating A is 0.20). If A wins a war with B, then A gets all of the disputed land (and B has none). If A loses to B then A gets none of the disputed land (so B has it all). Assume that the war will cost A an amount equal to the value of 20% of the land. [Technical note: Assume utilities are linear with value so that, for instance, 10% of land has a utility of 10; 80 percent of land has a utility of 80 and so forth.] What is A's expected utility from waging war against B? 10. Continuing with the previous problem. What is the maximum amount of land that B can control and that A can agree to as the division of control over the disputed territory so that A will not go ahead with its threat to go to war against B. (Hind: If A is indifferent between waging war and accepting a negotiated agreement, A will accept the negotiated agreement). Space to show additional work (labeled to link it to a question)

Answer 1

This graph indicates the range of outcomes, a) expected utility from war of 'A' = Probability of winning times U(% of land after winning) + Probability of losing times U(% of land after losing) Substituting all implies (0.80) times 100 + (0.20) times 0 = 80 + 0 = 80 expected utility from war of 'A' = 80. Expected control over land of 'A' = 80% therefore implies B can (100 - 80)% = 20% of land.