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} $

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