Problem
Let's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a contin¬ued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0.
Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader.
If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent.
If country A allows concession (A2), both in case of country A is amicable p(S1) and belligerent p(s2), outcome (C2) is realized.
Answer the following questions
A. What is the expected utility of action A1?
B. What is the expected utility of action A2?
C. What action should country A choose A1 or A2?
D. What action should country A choose if u(C2) were equal to 0.5 rather than 0.3 A1 or A2?
E. What action should country A choose if u(C2) were equal to 0.3 but p(S1) were equal to 0.25 (and p(S2) = 0.75) A1 or A2?