gambit-hp

Compute a Nash equilibrium in a strategic game using the homotopy method of Herings and Peeters [HerPee01].

The algorithm finds one equilibrium starting from any given prior distribution over strategies, which must have a unique best response for each player. Multiple prior distributions may be generated via the -n option or specified via the -s option; different priors 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.

-m

Specify the maximum regret criterion for acceptance as an approximate Nash equilibrium (default is 1e-8). See Acceptance criteria for approximate Nash equilibria for interpretation and guidance.

-n

Randomly generate the specified number of prior distributions. Mutually exclusive with -s.

-R

Seeds the random number generator used to generate prior distributions with the specified value, so that the sequence of priors 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 prior distributions over strategies. 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, --verbose

Show the prior distribution itself, tagged prior, followed by each point traced along the homotopy path, tagged with the homotopy parameter t in place of the NE tag. Note that the point at t=0 is the best response to the prior, and so is generally a pure strategy profile even when the prior itself is not. If this option is not specified, only the equilibrium found is reported.

-v, --version

Prints version information and exits.

Computing an equilibrium of the reduced strategic form of the example in Figure 2 of [Sel75], starting from the prior in which player 1 plays (0.5, 0.3, 0.2) and player 2 plays (0.6, 0.4):

$ echo "0.5,0.3,0.2,0.6,0.4" > prior.csv
$ gambit-hp -s prior.csv catalog/games/journals/ijgt/selten1975/fig2.efg
Compute a Nash equilibrium using the Herings-Peeters (2001) homotopy method
Gambit version |release|, Copyright (C) 1994-2026, The Gambit Project
This is free software, distributed under the GNU GPL

NE,1.000000,0.000000,0.000000,0.999976,0.000024