# The Lemke-Howson algorithm - exercises¶

1. Define the Lemke-Howson algorithm
2. Draw the best response polytopes and use the Lemke-Howson algorithm (with all possible starting labels) for the following games:
1. $A = \begin{pmatrix} 3 & -1\\ 2 & 7\end{pmatrix} \qquad B = \begin{pmatrix} -3 & 1\\ 1 & -6\end{pmatrix}$
2. $A = \begin{pmatrix} 2 & -1\\ 1 & 3\end{pmatrix} \qquad B = \begin{pmatrix} -2 & 2\\ 1 & -2\end{pmatrix}$
3. Use the tableaux representation to execute the Lemke-Howson algorithm (using starting label: 0) on the games of question 2.
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