gambit-liap

Compute Nash equilibria using function minimization. See the algorithm description for full details.

Changed in version 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.

Changed in version 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.

Changed in version 16.7.0: The -S switch has been removed. Since the introduction of -A in 16.5.0, the default (without -A) was already to compute using the strategic form for extensive games, making -S redundant.

-A

Added in version 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.

-d

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

-n

Specify the number of starting points to randomly generate. Mutually exclusive with -s.

-R

Seeds the random number generator used to generate starting points with the specified value, so that the sequence of points generated by -n can be reproduced across runs. If not specified, the generator is seeded from system entropy. Requires -n.

-i

Added in version 16.1.1.

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

-m

Added in version 16.2.0.

Specify the maximum regret criterion for acceptance as an approximate Nash equilibrium (default is 1e-4). See Acceptance criteria for approximate Nash equilibria for interpretation and guidance.

-h

Prints a help message listing the available options.

-q

Suppresses printing of the banner at program launch.

-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). Mutually exclusive with -n.

-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 the example in Figure 2 of [Sel75]:

$ gambit-liap catalog/games/journals/ijgt/selten1975/fig2.efg
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