gambit-lcp reads a two-playergame on standard input and computes Nash equilibria by finding solutions to a linear complementarity problem. For extensive games, the program uses the sequence form representation of the extensive game, as defined by Koller, Megiddo, and von Stengel, and applies the algorithm developed by Lemke. For strategic games, the program using the method of Lemke and Howson.
It is known that this method may not locate all equilibria in a game. Some equilibria in some games are not accessible using the path-following procedure implemented in this program.
-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.
-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.)
-PBy 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.)
-hPrints a help message listing the available options.
-qSuppresses printing of the banner at program launch.