h

t

H

3, 0

0, 2

T

0, 2

1, 0

If we call the row player A and the column player B, then the mixed-strategy Nash equilibrium is for A to pick H 1/2 of the time and T 1/2 of the time and for B to pick h 3/4 of the time and t 1/4 of the time. Let’s see the expected payoffs. A is going to get an expected payoff of [(3) * (1/2) * (3/4)] + [(0) * (1/2) * (1/4)] + [(0) * (1/2) * (3/4)] + [(1) * (1/2) * 1/4)] = 1.25 B is going to get [(0) * (1/2) * (3/4)] + [(2) * (1/2) * (1/4)] + [(2) * (1/2) * (3/4)] + [(0) * (1/2) * 1/4)] = 1