The famous British spy 007 has to choose one of four routes A, B, C, or D (liste

Question

The famous British spy 007 has to choose one of four routes A, B, C, or D (listed in order of speed in good conditions) to ski down a mountain. Fast routes are more susceptible to an avalanche At the same time, the notorious rival spy 001 has to choose whether to use Y or not to use X his valuable explosive to try to cause an avalanche to undermine 007's success. The payoffs to this game are as follows 007 X 0, 12 1,11 2, 10 3, 9 Y 6,0 5,12,4 0, 6 001 (a) Suppose that 001 choses to not use the explosives (i.e., chooses X) with probability p where 0 S p

Explanation / Answer

Given: the british spy 007 has to choose one routes of 4 of them.

(a) probability is given as p and the spy 007 will do as

If p1(x)>2/3, a; if p1(x)<2/3, p1(x) = 2/3

So 0 < q1, q3 <= 1.

(b) yes, 007 would be adivsed to not to take route B, because any combination with b would make the mixed strategy less than optimal so that's why spy 007 would be advised for same.

(c) if we refer to p1(x) = 2/3, 0 <= q1, q3<= 1, and many NE equilibrium are out there.

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