gambit-gnm

Compute Nash equilibria in a strategic game using a global Newton method. See the algorithm description 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.

-d

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

-h

Prints a help message listing the available options.

-n

Randomly generate the specified number of perturbation vectors. Mutually exclusive with -s.

-R

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

-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.

-m LAMBDA

Added in version 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.

-f FREQ

Added in version 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.

-i MAXITS

Added in version 16.2.0.

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

-c STEPS

Added in version 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.

-V, --verbose

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

-v, --version

Prints version information and exits.

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

$ gambit-gnm catalog/games/journals/ijgt/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

See also

gambit-ipa.