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Two countries, A and B, are at war. War is costly, but neither country wants to...

Two countries, A and B, are at war. War is costly, but neither country wants to be the first to surrender. At the start of each period, there is a peace conference in which the two countries independently and simultaneously tell an arbitrator whether they are willing to surrender (S) or prefer to keep fighting (F).Suppose that in any period, A says S with probability 1/4 while B says S with probability 1/3.

If either A or B (but not both) says S, the one that does not say S wins and the war ends in that period.

If both say S, then the war ends in that period with no winner.

If neither says S, the war continues to the next period.

Q1) In any given period, what is the probability that the war ends?

Q2) What is the probability that B wins the war?

Math   Statistics-And-Probability   
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