1. ## 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?

2. Originally Posted by Victor
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:
$\displaystyle \begin{bmatrix} & (1, even) & (1, odd) & (2, even) & (2, odd) \\ 1 & 1 & -1 & -1 & 1 \\ 2 & -1 & 1 & 1 & -1\end{bmatrix}$

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

Can you find a saddle point there?