Consider the following payoff matrix:

Image is a $2$ by $2$ matrix with entries from left$-$to$-$right, top$-$to$-$bottom: $5,7,6,2$

Which one of the following is correct?

Question $2$ options:

The game has no optimal pure strategy. The the optimal mixed strategy for Player $1$ is $(0\mathrm{.}833,0\mathrm{.}167)$ which results in an expected payoff of $4\mathrm{.}333.$

The game has no optimal pure strategy. The optimal mixed strategy for Player $1$ is $(0\mathrm{.}667,0\mathrm{.}333)$ which results in an expected payoff of $5\mathrm{.}333.$

The value of the game is $5,$ and the corresponding pure strategy pair is

$.$

The value of the game is $6,$ and the corresponding pure strategy pair is

$.$

The value of the game is between $[5,6],$ with the optimal mixed strategy for Player $2$ being $(0\mathrm{.}667,0\mathrm{.}333).$