Chapter 3. The Gambit tools

Gambit provides an array of programs for manipulating and analyzing games. This chapter describes these programs in detail.

3.1. Programs for computing Nash equilibria

Table of Contents
gambit-enumpure -- Searches for pure-strategy Nash equilibria in a game.
gambit-enumpoly -- Computes Nash equilibria in a game by solving polynomial systems
gambit-enummixed -- Computes Nash equilibria in a two-player strategic game using extreme point enumeration
gambit-gnm -- Computes Nash equilibria in a strategic game using a global Newton method
gambit-ipa -- Computes Nash equilibria in a strategic game using iterated polymatrix approximation
gambit-lcp -- Computes Nash equilibria in a two-player game by solving a linear complementarity program
gambit-lp -- Computes Nash equilibria in a two-player constant-sum game by solving a linear program
gambit-liap -- Computes Nash equilibria in a game using a function minimization approach
gambit-simpdiv -- Computes approximations to Nash equilibria in a strategic game using a simplicial subdivision approach
gambit-logit -- Computes the principal branch of the (logit) quantal response correspondence in a game

This section describes the implementations of various methods for computing Nash equilibria provided by Gambit. For a general overview of the formulations of the Nash equilibrium problem, see the survey of McKelvey and McLennan (1996) [McKMcL96].

By convention, these programs take an extensive or strategic game file on standard input, and output a list of equilibria computed. The equilibria computed are presented as a list of comma-separated probabilities, preceded by the tag "NE". Many of the programs optionally output additional information about the operation of the algorithm; these outputs have other, program-specific tags, described in the individual program documentation.