Rationalisation - Exercises

  1. Give the definition of a dominated strategy.
  2. Give the definition of a weakly dominated strategy.
  3. Give the defininition of common knowledge of rationality.
  4. For the following games predict rational behaviour or explain why this cannot be done:

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

    2. $ A = \begin{pmatrix} 2 & 1 & 3 & 17\\ 27 & 3 & 1 & 1\\ 4 & 6 & 7 & 18 \end{pmatrix} \qquad B = \begin{pmatrix} 11 & 9 & 10 & 22\\ 0 & 1 & 1 & 0\\ 2 & 10 & 12 & 0 \end{pmatrix} $

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

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

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