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Math Help - pure strategy

  1. #1
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    Unhappy pure strategy

    Hi i am stuck with pure strategies. I have attached the table that i have the question about. I was wondering how to show that the game attached has a solution in pure strategies.

    i have tried to work out the maximin and minimax as shown on the attached document. But wasnt too sure about the value of the game.

    can some one please help me with this.

    thanks
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  2. #2
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    A game has a solution with pure strategies if there is an element of the payoff matrix that is minimal in its row and maximal in its column. The value of the game is then the value of that element.

    In the example in the spreadsheet, the element in row A2 and column B3 has that property.

    An easy way to determine whether there is a solution with pure strategies is to circle the minimal element(s) in each row, and to put a square box round the maximal element(s) in each column. You then just have to look and see if there is an element that is both circled and boxed.
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  3. #3
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    Question pure stragies continued

    thank you for that definition, that was a big help.

    So for this case would the value of the game be =2, even though i got a maximin value of 5 and a minimax value of 2 (as shown in the attachment before)?

    Also how would i find the optimal pure strategy for each player?
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  4. #4
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    Quote Originally Posted by dopi View Post
    how would i find the optimal pure strategy for each player?
    The optimal pure strategy for A is always to go for option A2. The optimal pure strategy for B is always to go for option B3.
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