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Math Help - Game Theory- Values

  1. #1
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    Game Theory- Values

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

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



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

     H^{II}(p,q) = p_{1}(8-16q) + p_{2}(4-12q) +10q ...I need to find the values of  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!

    Attached Thumbnails Attached Thumbnails Game Theory- Values-game-theory-publish.jpg  
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