Support enumeration - exercises

1. Define the support of a strategy.
2. Obtain the supports for the following strategy vectors:
   1. $\sigma = (1, 0, 0, 0)$
   2. $\sigma = (.5, 0, .5, 0)$
   3. $\sigma = (.25, .25, .25, .25)$
3. Define a degenerate game.
4. Construct a degenerate $3\times 3$ game.
5. Describe the support enumeration algorithm.

6. Use support enumeration to find Nash equilibria for the following games:

   1. $ A = \begin{pmatrix} 3 & 3 & 2 \\ 2 & 1 & 3 \end{pmatrix} \qquad B = \begin{pmatrix} 2 & 1 & 3 \\ 2 & 3 & 2 \end{pmatrix} $

   2. $ A = \begin{pmatrix} 3 & -1\\ 2 & 7\end{pmatrix} \qquad B = \begin{pmatrix} -3 & 1\\ 1 & -6\end{pmatrix} $