Question

Jack and Jill have gone out for cycling and they have come to a place where the road is obstructed by a fallen tree. They can move the tree if both of them try. If none of them​ tries, they have to turn back and reach home very late.​ However, if one of them tries while the other does not​ help, the one who tries will have a muscle sprain and will not be able to move the tree. The matrix below shows the utility each of them derives in each situation. The first number listed in each cell is the payoff to the row player and the second number listed is the payoff to the column player.
Jill
Tries Does not try
Jill Tries 5 5
5 2
Does not try -2 -2
-5 -2
1. Refer to the scenario above. Jack will derive​ ________ units of utility if both of them try to move the tree.
A. 5
B. −5
C. −2
D. 10
2. Refer to the scenario above. Jack will derive​ ________ units of utility if Jill tries to move the tree while he does not try at all.
A. 5
B. −5
C. −2
D. 10
3. Refer to the scenario above. Jack and Jill will derive maximum utility​ if:
A. Neither of them tries to move the tree.
B. Jack tries to move the​ tree, while Jill does not.
C. Jill tries to move the​ tree, while Jack does not.
D. Both of them try to move the tree.
4. Refer to the scenario above. Which of the following is true in this​ case?
A. Jill is better off by not trying if Jack tries to move the tree.
B. Jack is better off by trying to move the tree if Jill does not try at all.
C. Jack is better off by trying to move the tree if Jill tries to move the tree.
D. Jill is better off by trying to move the tree if Jack does not try at all.
5. Refer to the scenario above. This game​ ________.
A. does not have a dominant strategy equilibrium
B. does not have a Nash equilibrium
C. has a unique Nash equilibrium
D. has a unique dominant strategy equilibrium

Answer 1

Answer: See explanation

Explanation:

1. Refer to the scenario above. Jack will derive​ (5) units of utility if both of them try to move the tree.

The answer to the question will be the first payoff in the matrix and this is 5.

2. Refer to the scenario above. Jack will derive (-2) units of utility if Jill tries to move the tree while he does not try at all.

This will be gotten from the second cell of the matrix. The answer is-2.

3. Refer to the scenario above. Jack and Jill will derive maximum utility​ if (both of them try to move the tree).

Here, the payoff matrix has a maximum value of 5 and at this point, both of them can get maximum utility. Therefore, the correct option is D.

4. The true statement is that "Jack is better off by trying to move the tree if Jill tries to move the tree". Therefore, the correct option is C.

5. The scenario above indicates that the game does not have a dominant strategy equilibrium as it is dependent on the strategy of other players. Therefore, the correct option is A.