Question

Two players, 1 and 2, play the matching pennies game represented in the following payoffs
matrix:
Player 2
L R
Player 1 L 1;- 1 -1; 1
H -1; 1 1;-1

1. How many Nash equilibria (in pure and mixed strategies) exist?
2. Compute the best-reply functions and provide a graphical representation of the equilibrium

Answer 1

$$Solution$$

For the even player, the expected payoff on player 1 is

$+1.(x-1).(1-x)\ and\ for\ player\ 2\ -1.x+1.(1-x) and\ those\ must\ be\ equal,\ so,\ x=0.5\\ For\ the\ odd\ player\ the\ expected\ payoff\ when\ player\ 1\ plays,\ +1.y+1.(1-y)\ and\ those\ must\ be\ equal\ so\ ,y=0.5$

Note: x is player 1's probability of odd and y is player 1's probability of Even.