Chadwick Gambit: Software Tools for Game Theory
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gambit-enumpure: Enumerate pure-strategy equilibria of a game#

gambit-enumpure reads a game on standard input and searches for pure-strategy Nash equilibria.

Changed in version 14.0.2: The effect of the -S switch is now purely cosmetic, determining how the equilibria computed are represented in the output. Previously, -S computed using the strategic game; if this was not specified for an extensive game, the agent form equilibria were returned.

-S#

Report equilibria in reduced strategic form strategies, even if the game is an extensive game. By default, if passed an extensive game, the output will be in behavior strategies. Specifying this switch does not imply any change in operation internally, as pure-strategy equilibria are defined in terms of reduced strategic form strategies.

-D#

New in version 14.0.2.

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.

-A#

New in version 14.0.2.

Report agent form equilibria, that is, equilibria which consider only deviations at one information set. Only has an effect for extensive games, as strategic games have only one information set per player.

-P#

By default, the program computes all pure-strategy Nash equilibria in an extensive game. This switch instructs the program to find only pure-strategy Nash 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 the pure-strategy equilibria of extensive game e02.efg, the example in Figure 2 of Selten (International Journal of Game Theory, 1975):

$ gambit-enumpure e02.efg
Search for Nash equilibria in pure strategies
Gambit version 16.2.0, Copyright (C) 1994-2024, The Gambit Project
This is free software, distributed under the GNU GPL

NE,1,0,0,0,1,0

With the -S switch, the set of equilibria returned is the same, except expressed in strategic game strategies rather than behavior strategies:

$ gambit-enumpure -S e02.efg
Search for Nash equilibria in pure strategies
Gambit version 16.2.0, Copyright (C) 1994-2024, The Gambit Project
This is free software, distributed under the GNU GPL

NE,1,0,0,1,0

The -A switch considers only behavior strategy profiles where there is no way for a player to improve his payoff by changing action at only one information set; therefore the set of solutions is larger:

$ gambit-enumpure -A e02.efg
Search for Nash equilibria in pure strategies
Gambit version 16.2.0, Copyright (C) 1994-2024, The Gambit Project
This is free software, distributed under the GNU GPL

NE,1,0,1,0,1,0
NE,1,0,1,0,0,1
NE,1,0,0,1,1,0
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