Chadwick Gambit: Software Tools for Game Theory
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gambit-lp: Compute equilibria in a two-player constant-sum game via linear programming#

gambit-lp reads a two-player constant-sum game on standard input and computes a Nash equilibrium by solving a linear program. The program uses the sequence form formulation of Koller, Megiddo, and von Stengel [KolMegSte94] for extensive games.

While the set of equilibria in a two-player constant-sum strategic game is convex, this method will only identify one of the extreme points of that set.

-d#

By 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 an equilibrium. 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 the specified number of digits.

-S#

By default, the program uses behavior strategies for extensive games; this switch instructs the program to use reduced strategic game strategies for extensive games. (This has no effect for strategic games, since a strategic game is its own reduced strategic game.)

-D#

New in version 14.0.3.

The default output format for computed equilibria is a comma-separated list of strategy or action probabilities, suitable for postprocessing by automated tools. Specifying -D instead causes the program to output greater detail on each equilbrium profile computed.

-P#

By default, the program computes Nash equilibria in an extensive game. This switch instructs the program to find only equilibria which are subgame perfect. (This has no effect for strategic games, since there are no proper subgames of a strategic game.)

-h#

Prints a help message listing the available options.

-q#

Suppresses printing of the banner at program launch.

Computing an equilibrium of the game 2x2const.nfg, a game with two players with two strategies each, with a unique equilibrium in mixed strategies:

$ gambit-lp 2x2const.nfg
Compute Nash equilibria by solving a linear program
Gambit version 16.2.0, Copyright (C) 1994-2024, The Gambit Project
This is free software, distributed under the GNU GPL

NE,1/3,2/3,1/3,2/3
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