Let the matrix in the attached picture represent a 2 players game.

In the mixing game, find the value that thecolumns player canassure to himself and a strategy of the rows-player that prevents the columns-player to get more than the value.

If $\displaystyle p_{1},p_{2},1-p_{1}-p_{2}$ are the strategies of the rows player and $\displaystyle 1,1-q$ are the strategies of the columns player, then:

$\displaystyle H^{II}(p,q) = p_{1}(8-16q) + p_{2}(4-12q) +10q $...I need to find the values of $\displaystyle p_{1},p_{2}$ that minimize this expression...But have no idea how to do it...

Hope you'll be able to help me

Thanks!