gambit-enummixed reads a two-player game on standard input and computes Nash equilibria using extreme point enumeration.
This program searches for all Nash equilibria in a two-player strategic game by enumerating all possible extreme points of the convex components of Nash equilibria. These extreme points are exactly those that could in principle be visited by the path-following procedure of Lemke and Howson; however, the enumeration method visits all such points (whereas some points are not accessible via the method of Lemke and Howson).
In general, the set of Nash equilibria in a two-player strategic game can be expressed as the union of convex sets. The equilibrium profiles generated by this program are the extreme points of those convex sets.
-d DECIMALSBy default, this program computes using exact rational arithmetic. Since the extreme points computed by this method are guaranteed to be rational when the payoffs in the game are rational, this permits exact computation of the equilibrium set. Computation using rational arithmetic is in general slow, however. For most games, acceptable results can be obtained by computing using the computer's native floating-point arithmetic. Using this flag enables computation in floating-point, and expresses all output using decimal representations with DECIMALS digits.
-cThe program outputs the extreme equilibria as it finds them, prefixed by the tag NE. If this option is specified, once all extreme equilbria are identified, the program computes the convex sets which make up the set of equilibria. The program then additionally outputs each convex set, prefixed by convex-N, where N indexes the set. The set of all equilibria, then, is the union of these convex sets.
-hPrints a help message listing the available options.
-qSuppresses printing of the banner at program launch.