Question

3. Consider the following stag hunt game. Two hungry hunters go to the woods with the aim of catching a stag, or at least a hare. They can catch a stag only if both remain alert and devote their time and energy to catching it. Catching a hare is less demanding and does not require the cooperation of the other hunter. Each hunter prefers half a stag to a hare. Letting S denote the action of going after the stag, and the action of catching a hare, we can represent this game by the following: 2,2 н 0,1 1.1 Find all pure and mixed Nash equilibria of this game by constructing the best response correspondences of the players.

Answer 1

Pure Nash Equilibria:

Condition 1:- If hunter 2 catches stag, then hunter 1 is having two options either can go for stag or hare. So, we need to see which will give hunter 1 the higher pay off. For stag he will get pay off (2) and for hare he will get pay off (1). Hence hunter 1 is getting higher pay off at stag in this case.

Condition 2:- If hunter 2 catches hare, then hunter 1 is having two options either can go for stag or hare. So, we need to see which will give hunter 1 the higher pay off. For stag he will get pay off (0) and for hare he will get pay off (1). Hence hunter1 is getting higher pay off at hare in this case.

Condition 3:- If hunter 1 catches stag, then hunter 2 is having two options either can go for stag or hare. So, we need to see which will give hunter 2 the higher pay off. For stag he will get pay off (2) and for hare he will get pay off (1). Hence hunter 2 is getting higher pay off at stag in this case.

Condition 4:- If hunter 1 catches hare, then hunter 2 is having two options either can go for stag or hare. So, we need to see which will give hunter 2 the higher pay off. For stag he will get pay off (0) and for hare he will get pay off (1). Hence hunter 2 is getting higher pay off at hare in this case.

In this game, there are two pure nash equilbria (2,2) and (1,1) in which both hunters are getting the higher pay off. Hence , they both are giving their optimal efforts on the basis of individual deviation.