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Math Help - Zero Sum Games

  1. #1
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    Zero Sum Games

    Victor and David each have two cards, a one (or ace) and a two. They
    each select one of their cards, with their choices unknown to the
    opponent, and then they will compare the cards. Before they compare
    the cards, Victor gets to call “even” or “odd”. Victor wins if the sum of
    the face values of the selected cards is of the parity he has called, and
    if not, David wins. Model the game as a 2-person zero-sum game. Does
    the game have a saddle point?
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  2. #2
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    Quote Originally Posted by Victor View Post
    Victor and David each have two cards, a one (or ace) and a two. They
    each select one of their cards, with their choices unknown to the
    opponent, and then they will compare the cards. Before they compare
    the cards, Victor gets to call “even” or “odd”. Victor wins if the sum of
    the face values of the selected cards is of the parity he has called, and
    if not, David wins. Model the game as a 2-person zero-sum game. Does
    the game have a saddle point?
    So Victor has four plays:
    (1, even), (1, odd), (2, even), and (2, odd)
    (i.e. play that card, call that parity)
    while David has two1) and (2)
    It's easy to write out a table for the game:
    \begin{bmatrix}  & (1, even) & (1, odd) & (2, even) & (2, odd) \\ 1 & 1 & -1 & -1 & 1 \\ 2 & -1 & 1 & 1 & -1\end{bmatrix}

    where 1 is "Victor wins" and -1 is "David wins".

    Can you find a saddle point there?
    Last edited by HallsofIvy; May 12th 2009 at 09:35 AM.
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