gambit-liap: Compute Nash equilibria using function minimization#
Changed in version 16.2.0: The Lyapunov function is now normalized to be independent of the scale of the payoffs of the game; therefore multiplying or dividing all payoffs by a common factor will not affect the output of the algorithm.
The criterion for accepting whether a local constrained minimizer of the Lyanunov function is an approximate Nash equilibrium is specified in terms of the maximum regret. This regret is interpreted as a fraction of the difference between the maximum and minimum payoffs in the game.
Changed in version 16.5.0: The -A switch has been introduced to be explicit in choosing to compute agent Nash equilibria. The default is now to compute using the strategic form even for extensive games.
- -A#
Added in version 16.5.0.
Report agent Nash equilibria, that is, equilibria which consider only deviations at a single information set at a time. Only has an effect for extensive games, as strategic games have only one information set per player.
- -d#
Express all output using decimal representations with the specified number of digits.
- -n#
Specify the number of starting points to randomly generate.
- -i#
Added in version 16.1.1.
Specify the maximum number of iterations in function minimization (default is 1000).
- -m#
Added in version 16.2.0.
Specify the maximum regret criterion for acceptance as an approximate Nash equilibrium (default is 1e-4). See pygambit-nash-maxregret for interpretation and guidance.
- -h#
Prints a help message listing the available options.
- -q#
Suppresses printing of the banner at program launch.
- -s#
Specifies a file containing a list of starting points for the algorithm. 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).
- -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.)
- -v#
Sets verbose mode. In verbose mode, initial points, as well as points at which the minimization fails at a constrained local minimum that is not a Nash equilibrium, are all output, in addition to any equilibria found.
Computing an equilibrium in mixed strategies of e02.efg, the example in Figure 2 of Selten
(International Journal of Game Theory, 1975)
$ gambit-liap e02.nfg Compute Nash equilibria by minimizing the Lyapunov function Gambit version 16.5.0, Copyright (C) 1994-2026, The Gambit Project This is free software, distributed under the GNU GPL
NE,0.998701,0.000229,0.001070,0.618833,0.381167