.. _gambit-liap:

:program:`gambit-liap`: Compute Nash equilibria using function minimization
===========================================================================

:ref:`Algorithm description <liap>`

.. versionchanged:: 16.2.0

   The Lyapunov function is now normalized to be independent of the
   scale of the payoffs of the game; therefore multiplying or dividing
   all payoffs by a common factor will not affect the output of the
   algorithm.

   The criterion for accepting whether a local constrained minimizer
   of the Lyanunov function is an approximate Nash equilibrium is specified
   in terms of the maximum regret.  This regret is interpreted as a fraction
   of the difference between the maximum and minimum payoffs in the game.

.. versionchanged:: 16.5.0

   The `-A` switch has been introduced to be explicit in choosing to compute
   agent Nash equilibria.  The default is now to compute using the strategic
   form even for extensive games.


.. program:: gambit-liap

.. cmdoption:: -A

   .. versionadded:: 16.5.0

   Report agent Nash equilibria, that is, equilibria which consider
   only deviations at a single information set at a time.  Only has
   an effect for extensive games, as strategic games have only
   one information set per player.

.. cmdoption:: -d

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

.. cmdoption:: -n

   Specify the number of starting points to randomly generate.

.. cmdoption:: -i

   .. versionadded:: 16.1.1

   Specify the maximum number of iterations in function minimization (default is 1000).

.. cmdoption:: -m

   .. versionadded:: 16.2.0

   Specify the maximum regret criterion for acceptance as an approximate Nash equilibrium
   (default is 1e-4).  See :ref:`pygambit-nash-maxregret` for interpretation and guidance.

.. cmdoption:: -h

   Prints a help message listing the available options.

.. 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:: -S

   By default, the program uses behavior strategies for extensive
   games; this switch instructs the program to use reduced strategic game
   strategies for extensive games. (This has no effect for strategic
   games, since a strategic game is its own reduced strategic game.)

.. cmdoption:: -v

   Sets verbose mode. In verbose mode, initial points, as well as
   points at which the minimization fails at a constrained local minimum
   that is not a Nash equilibrium, are all output, in addition to any
   equilibria found.

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

   $ gambit-liap e02.nfg
   Compute Nash equilibria by minimizing the Lyapunov function
   Gambit version |release|, Copyright (C) 1994-2026, The Gambit Project
   This is free software, distributed under the GNU GPL

   NE,0.998701,0.000229,0.001070,0.618833,0.381167