Countries A and B are deciding to divide $100 between them. If they cant reach and agreement, they go to war, in which case A wins with probability (3/4) and B wins with probability (1/4). If a country wins, it gets the entire $100, and it gets $0 if it loses. If they go to war, each country pays a cost of war of $10.
a) What is country A's expected utility for war?
b) What is country B's expected utility for war?
c) Is there any peaceful division of the $100 that both sides would prefer to war? If so, list one of them
d) Now suppose that the leafer of country A is facing domestic troubles and if he fights a war and wins it, he will get an additional $40 worth of benefits because his reelection will guaranteed.
(i) Recalculate A's expected utility for war under this new senario, and
(ii) re-answer question (c) under this new scenario