Finding Nash Equilibriums

Question

Nash Equilibrium for this Normal Game

1,1 2,4 1,4 0,8 1,1 1,1 3,0 0,0 7,0

I know for sure that the Nash Equilibrium : (2,4) Is (3,0) and (7,0) also Nash Equilibriums?

Answer 1

To determine if a point is a Nash Equilibrium, we see if a player will deviate given that the other player holds fixed. So consider $(3, 0)$. Suppose player one picks the bottom row. Will player two change columns? Player two will be no better off by doing such, but will also be no worse off. So $(3, 0)$ is a candidate for a Nash Equilibrium. Now suppose player two is fixed at column one. Clearly, player one won't change rows, as that would make him worse off. So $(3, 0)$ is a Nash Equilibrium.

The same analysis yields that $(7, 0)$ is also a Nash Equilibrium.