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

gambit-ipa reads a game on standard input and computes Nash equilibria using an iterated polymatrix approximation approach developed by Govindan and Wilson [GovWil04]. This program is based on the Gametracer 0.2 implementation by Ben Blum and Christian Shelton.

The algorithm takes as a parameter a mixed strategy profile. This profile is interpreted as defining a ray in the space of games. The profile must have the property that, for each player, the most frequently played strategy must be unique.

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.

-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.

-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).

Computing an equilibrium of 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 16.2.0, Copyright (C) 1994-2024, The Gambit Project
This is free software, distributed under the GNU GPL

NE,1.000000,0.000000,0.000000,1.000000,0.000000

See also

gambit-gnm: Compute Nash equilibria in a strategic game using a global Newton method.