Editing Nash equilibrium (section)

=== Examples ===
{| class="wikitable floatright" style="text-align:center; font-size:95%; margin-left:1.5em;"
|+ Matching pennies
!scope="col" rowspan="2"| Player A<br/> plays
!scope="row" colspan="2" | Player B plays
|-
!scope="col" | H
!scope="col"| T
|-
!scope="row"| H
| −1, +1
| +1, −1
|-
!scope="row"| T
| +1, −1
| −1, +1
|}

In the matching pennies game, player A loses a point to B if A and B play the same strategy and wins a point from B if they play different strategies. To compute the mixed-strategy Nash equilibrium, assign A the probability <math>p</math> of playing H and <math>(1-p)</math> of playing T, and assign B the probability <math>q</math> of playing H and <math>(1-q)</math> of playing T.

<math display="block">\begin{align}
&\mathbb{E}[\text{payoff for A playing H}] = (-1)q + (+1)(1 - q) = 1 - 2q, \\
&\mathbb{E}[\text{payoff for A playing T}] = (+1)q + (-1)(1 - q) = 2q - 1, \\
&\mathbb{E}[\text{payoff for A playing H}] = \mathbb{E}[\text{payoff for A playing T}] \implies 1 - 2q = 2q - 1 \implies q = \frac{1}{2}. \\
&\mathbb{E}[\text{payoff for B playing H}] = (+1)p + (-1)(1 - p) = 2p - 1, \\
&\mathbb{E}[\text{payoff for B playing T}] = (-1)p + (+1)(1 - p) = 1 - 2p, \\
&\mathbb{E}[\text{payoff for B playing H}] = \mathbb{E}[\text{payoff for B playing T}] \implies 2p - 1 = 1 - 2p \implies p = \frac{1}{2}.
\end{align}</math>

Thus, a mixed-strategy Nash equilibrium in this game is for each player to randomly choose H or T with <math>p = \frac{1}{2}</math> and <math>q = \frac{1}{2}</math>.