.. _gambit-ipa:

:program:`gambit-ipa`: Compute Nash equilibria in a strategic game using iterated polymatrix approximation
==========================================================================================================

:ref:`Algorithm description <ipa>`

The algorithm finds at most one equilibrium starting from any given profile.
Multiple starting profiles may be generated via the `-n` option or specified
via the `-s` option; different starting profiles may result in different
equilibria being found.


.. program:: gambit-ipa

.. cmdoption:: -d

   Express all output using decimal representations
   with the specified number of digits.

.. cmdoption:: -h

   Prints a help message listing the available options.

.. cmdoption:: -n

   Randomly generate the specified number of perturbation vectors.

.. cmdoption:: -q

   Suppresses printing of the banner at program launch.

.. cmdoption:: -s

   Specifies a file containing a list of starting points
   for the algorithm. The format of the file is comma-separated values,
   one mixed strategy profile per line, in the same format used for
   output of equilibria (excluding the initial NE tag).


Computing an equilibrium of :download:`e02.nfg <../contrib/games/e02.nfg>`,
the reduced strategic form of the example in Figure 2 of Selten
(International Journal of Game Theory, 1975)

   $ gambit-ipa e02.nfg
   Compute Nash equilibria using iterated polymatrix approximation
   Gametracer version 0.2, Copyright (C) 2002, Ben Blum and Christian Shelton
   Gambit version |release|, Copyright (C) 1994-2026, The Gambit Project
   This is free software, distributed under the GNU GPL

   NE,1.000000,0.000000,0.000000,1.000000,0.000000



.. seealso::

   :ref:`gambit-gnm`.