Max-Min Strategy equal pay-offs

Question

I have this pay-off matrix above which i try to find its max-min strategies but when i apply the max-min rule pay-offs are equal so i kinda get confused since i am a newbie to game theory. I would be appreciated if you can help me about this.

Answer 1

you have:\begin{array}{c|c}1\setminus2&L&R\\\hline L&2,-2&-2, 2\\\hline R&-2, 2&2,-2\end{array} first let's change it to:\begin{array}{c|c}1\setminus2&L&R\\\hline L&2&-2\\\hline R&-2&2\end{array} where the number is the cost from player $(2)$ to player $(1)$

Now let's say that for player $(1)$ there is $(p)$ chance to chose $L$ therefore $(1-p)$ for $R$.

so if $(2)$ plays $L$ $(1)$ gain is: $2p-2(1-p)$

and if $(2)$ plays $R$ $(1)$ gain is: $-2p+2(1-p)$

therefore:$$-2p+2(1-p)=2p-2(1-p)\implies 0=0$$this is probably not what you thought you will get but this actually is the answer, it implies that there is no dominant strategy. i recommend to read a bit here: link

it explain a bit about the meaning behind minimax strategy and have a real nice visualize