Solve with Lemke Howson
=======================

One of the algorithms implemented in :code:`Nashpy` is :ref:`lemke-howson`. This
algorithm does not return **all** equilibria and takes an input argument::

    >>> import nashpy as nash
    >>> import numpy as np
    >>> A = np.array([[1, -1], [-1, 1]])
    >>> matching_pennies = nash.Game(A)
    >>> matching_pennies.lemke_howson(initial_dropped_label=0)
    (array([0.5, 0.5]), array([0.5, 0.5]))

The :code:`initial_dropped_label` is an integer between :code:`0` and
:code:`sum(A.shape) - 1`. To iterate over all possible labels use the
:code:`lemke_howson_enumeration` which returns a generator::

    >>> equilibria = matching_pennies.lemke_howson_enumeration()
    >>> for eq in equilibria:
    ...     print(eq)
    (array([0.5, 0.5]), array([0.5, 0.5]))
    (array([0.5, 0.5]), array([0.5, 0.5]))
    (array([0.5, 0.5]), array([0.5, 0.5]))
    (array([0.5, 0.5]), array([0.5, 0.5]))

Note that this algorithm is not guaranteed to find **all** equilibria but is
an efficient way of finding **an** equilibrium.