gambit-liap reads a game on standard input and computes approximate Nash equilibria using a function minimization approach.
This procedure searches for equilibria by generating random starting points and using conjugate gradient descent to minimize the Lyapunov function of the game. This function is a nonnegative function which is zero exactly at strategy profiles which are Nash equilibria.
Note that this procedure is not globally convergent. That is, it is not guaranteed to find all, or even any, Nash equilibria.
-d DECIMALSExpress all output using decimal representations with DECIMALS digits.
-hPrints a help message listing the available options.
-n COUNTRandomly generate COUNT starting points.
-qSuppresses printing of the banner at program launch.
-s FILESpecifies 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).
-SBy 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.)
-vSets 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.