Economics Homework Help

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 0 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!)

1.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.)

2.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!)

3.(from the week 6 lectures) Use opponent’s indifference to find an expression for P.

4.Plug 2 into this formula to verify that your answer for n = 2 is the same as in part “a.”