Plotting the best response

Question

Observe the following matrix;

The pure strategy and mixed strategy nash equilibria are

The best response plot is given below

Can someone explain how this graph was plotted. I would much appreciate any assistance given, Thanks in advance

Answer 1

Strategies $R$ and $B$ are strictly dominated ($R$ is strictly dominated by any mixed strategy between $L$ and $C$ that gives $C$ probability strictly larger than $\frac{1}{2}$ and strictly smaller than $1$). Once you eliminate $R$ and $B$, it is a simple game whose way to solve it can be found in any undergraduate game theory textbook.

In this case $p$ is the probability that Player $1$ attaches to $T$ (hence, $1-p$ to $M$) and $q$ is the probability that Player $2$ attaches to $L$ (hence, $1-q$ to $C$). When $q$ is higher than $\frac{1}{4}$ Player $1$'s best response is playing $p=0$. When $q$ is smaller than $\frac{1}{4}$ Player $1$'s best response is playing $p=1$. And when $q=\frac{1}{4}$ then Player $1$ is indifferent between $T$ and $M$ and any value of $p$ is a best response. Player $2$'s best response correspondence is plotted similarly.