Suppose once they are out in the forest, each of a village's n hunters can choose to pursue a hare or a mammoth. If any hunter chooses to pursue a hare, they will always have success, and will get a payoff of 1, because the hare will provide a little food for each person in the hunter's family. If a hunter chooses to pursue a mammoth, they will get a payoff of O if no other hunter also chooses to pursue a mammoth, because it takes at least two hunters to bring down a mammoth. If at least one other hunter chooses to pursue a mammoth, they get a payoff of 4, because a mammoth provides more food than all the hunters' families can eat. (We are assuming that successful mammoth hunters don't share with hare hunters and vice versa!) A. Consider the case where n 2. What are the mixed strategy Nash equilibria of the game? (HINT: draw a matrix and solve for all MSNE.) B. Now consider the general case with any value of n. Suppose that each hunter decides to pursue a mammoth with probability P and to pursue a hare with probability 1-P. If hunter i pursues a mammoth, what is the probability that at least one of the other n-1 hunters will pursue a mammoth? (HINT: this is just a probability question, and there was a question similar to this on PS1!) C. (from the week 6 lectures) Use opponent's indifference to find an expression for P. D. Plug 2 into this formula to verify that your answer for n= 2 is the same as in part "a."
Suppose once they are out in the forest, each of a village's n hunters can choose to pursue a hare or a mammoth. If any hunter chooses to pursue a hare, they will always have success, and will get a payoff of 1, because the hare will provide a little food for each person in the hunter's family. If a hunter chooses to pursue a mammoth, they will get a payoff of O if no other hunter also chooses to pursue a mammoth, because it takes at least two hunters to bring down a mammoth. If at least one other hunter chooses to pursue a mammoth, they get a payoff of 4, because a mammoth provides more food than all the hunters' families can eat. (We are assuming that successful mammoth hunters don't share with hare hunters and vice versa!) A. Consider the case where n 2. What are the mixed strategy Nash equilibria of the game? (HINT: draw a matrix and solve for all MSNE.) B. Now consider the general case with any value of n. Suppose that each hunter decides to pursue a mammoth with probability P and to pursue a hare with probability 1-P. If hunter i pursues a mammoth, what is the probability that at least one of the other n-1 hunters will pursue a mammoth? (HINT: this is just a probability question, and there was a question similar to this on PS1!) C. (from the week 6 lectures) Use opponent's indifference to find an expression for P. D. Plug 2 into this formula to verify that your answer for n= 2 is the same as in part "a."
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Suppose once they are out in the forest, each of a village's n hunters can choose
to pursue a hare or a mammoth. If any hunter chooses to pursue a hare, they will
always have success, and will get a payoff of 1, because the hare will provide a
little food for each person in the hunter's family. If a hunter chooses to pursue a
mammoth, they will get a payoff of O if no other hunter also chooses to pursue a
mammoth, because it takes at least two hunters to bring down a mammoth. If at
least one other hunter chooses to pursue a mammoth, they get a payoff of 4,
because a mammoth provides more food than all the hunters' families can eat.
(We are assuming that successful mammoth hunters don't share with hare
hunters and vice versa!)
A. Consider the case where n = 2. What are the mixed strategy Nash equilibria
of the game? (HINT: draw a matrix and solve for all MSNE.)
B. Now consider the general case with any value of n. Suppose that each hunter
decides to pursue a mammoth with probability P and to pursue a hare with
probability 1-P. If hunter i pursues a mammoth, what is the probability that
at least one of the other n-1 hunters will pursue a mammoth? (HINT: this is
just a probability question, and there was a question similar to this on PS1!)
C. (from the week 6 lectures) Use opponent's indifference to find an expression
for P.
D. Plug 2 into this formula to verify that your answer for n = 2 is the same as in
part "a."
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