Find nash equilibrium in which player plays pure strategy

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Reference no: EM132217922

Question - On Her Majesty's Secret Service

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
		A	B	C	D
001	X	0, 12	1, 11	2, 10	3, 9
001	Y	6, 0	5, 1	2, 4	0, 6

(a) Suppose that 001 choses to not use the explosives (i.e., chooses X) with probability p where 0 ≤ p ≤ 1 and choses to use the explosives (i.e., chooses Y) with probability 1 - p. What will 007 do when p < 2/3; when p = 2/3; and p > 2/3. (Hint: construct the best response of 007 - BR₀₀₇(p)).

(b) Suppose that you are Q, the famous technical advisor to MI-6. Are there any routes you would advise 007 certainly not to take? Explain your answer.

(c) The gripped viewer of this epic drama is trying to figure out what will happen. Find a Nash equilibrium in which one player plays a pure strategy's and the other player plays a mixed strategy. Find a different mixed-strategy equilibrium in which that pure strategy's is assigned zero weight. Are there any other equilibria?

Reference no: EM132217922

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