Question

18.7 Homework • Unanswered How many Nash equilibria are there in the game below? Person 2 Low Med High 3,0 4,1 5,2 2,2 3,4 4,5 1,6 2,5 3,4 Low Med. High Person 1 ] |

Answer 1

First try to understand what is the meaning of each payoff in each box in the matrix present above. If person 2 chooses low and person 1 also chooses low, there is payoff of (3,0) where the payoff 3 represents payoff of player 1 while 0 represents payoff for player 2.

If Person 1 chooses low, person 2 will choose high as it gives the maximum payoff of 2 among 0/1/2.

If Person 1 chooses med., person 2 will choose high as it gives the maximum payoff of 5 among 2/4/5.

If Person 1 chooses high, person 2 will choose low as it gives the maximum payoff of 6 among 6/5/4.

There is no dominant strategy for person 2 as it chooses among high and low as person 1 changes their move.

If person 2 chooses low, person 1 will choose low as it gives maximum payoff of 3 among 3/2/1.

If person 2 chooses med., person 1 will choose low as it gives maximum payoff of 4 among 4/3/2.

If person 2 chooses high, person 1 will choose low as it gives maximum payoff of 5 among 5/4/3.

There is a dominant strategy of person 1 by choosing low in every case possible no matter what person 2 does.

For a Nash equilibrium to be present, both person must have dominant strategy. As person 2 does not have dominant strategy, there is no Nash equilibrium.