D
Dibya
Guest
On Her Majesty’s Secret Service. The famous British spy 001 has to choose one of four routes a,b,c and d(listed in order of spend in good condition) to ski down a mountain. Fast routes are more likely to be hit by an avalanche. At the same time, the notorious rival spy 002 whether to use (“y”) or not to use (“x”) his valuable explosive to cause an avalanche. The payoff to this game are as follows.
002
001XY
A12,00.6
B11,1 1,5
C10,24,2
D9,36,0
a.Let p1 (x) be the probability assigned by 001’s belief to oo2’s playing x. explain what 001 should do if p1(x)>2/3; if p1(x) <2/3 and p1(x)=2/3 ?
b.Suppose you are Mr. Queue , the Yale- educated technical advisor to British military intelligence. Are there any routes you would advise 001 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 Ч. Find a different mixed strategy equilibrium in which that pure strategy s is assigned zero weight ? are there any other equilibria?
002
001XY
A12,00.6
B11,1 1,5
C10,24,2
D9,36,0
a.Let p1 (x) be the probability assigned by 001’s belief to oo2’s playing x. explain what 001 should do if p1(x)>2/3; if p1(x) <2/3 and p1(x)=2/3 ?
b.Suppose you are Mr. Queue , the Yale- educated technical advisor to British military intelligence. Are there any routes you would advise 001 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 Ч. Find a different mixed strategy equilibrium in which that pure strategy s is assigned zero weight ? are there any other equilibria?