.. _gambit-gnm:

:program:`gambit-gnm`
=====================

Compute Nash equilibria in a strategic game using a global Newton method.
See the :ref:`algorithm description <gnm>` for full details.

The algorithm finds a subset of equilibria 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
subsets of equilibria being found.


.. program:: gambit-gnm

.. 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).

.. cmdoption:: -m LAMBDA

    .. versionadded:: 16.2.0

   Specifies the value of lambda at which to assume no more equilibria
   are accessible via the specified ray, and terminate tracing.
   Must be a negative number; default is -10.

.. cmdoption:: -f FREQ

    .. versionadded:: 16.2.0

   Specifies the frequency to run a local Newton method step.  This is
   a correction step that reduces accumulated errors in the path-following.
   Default is 3.

.. cmdoption:: -i MAXITS

    .. versionadded:: 16.2.0

   Specifies the maximum number of iterations in a local Newton method step.
   Default is 10.

.. cmdoption:: -c STEPS

    .. versionadded:: 16.2.0

   Specifies the number of steps to take within a support cell.  Larger values
   trade off speed for security in tracing the path.  Default is 100.

.. cmdoption:: -v

   Show intermediate output of the algorithm.  If this option is
   not specified, only the equilibria found are reported.

Computing an equilibrium of
the reduced strategic form of the example in Figure 2 of [Sel75]_::

   $ gambit-gnm catalog/selten1975/fig2.efg
   Compute Nash equilibria using a global Newton method
   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,1,0,2.99905e-12,0.5,0.5


.. seealso::

   :ref:`gambit-ipa`.