gambit-enumpoly reads a strategic game on standard input and computes Nash equilibria by solving systems of polynomial equations and inequalities.
This program searches for all Nash equilibria in a strategic game using a support enumeration approach. This approach computes all the supports which could, in principle, be the support of a Nash equilibrium, and then searches for a totally mixed equilibrium on that support by solving a system of polynomial equalities and inequalities formed by the Nash equilibrium conditions. The ordering of the supports is done in such a way as to maximize use of previously computed information, making it suited to the computation of all Nash equilibria.
When the verbose switch -v is used, the program outputs
each support as it is considered. The supports are presented as
a comma-separated list of binary strings, where each entry represents
one player. The digit 1 represents a strategy which is present in the
support, and the digit 0 represents a strategy which is not present.
Each candidate support is printed with the label "candidate,".
Note that the subroutine to compute a solution to the system of polynomial
equations and inequalities will fail in degenerate cases. When the
verbose switch -v is used, these supports are identified
on standard output with the label "singular,". It is possible
that there exist equilibria, often a connected component of equilibria,
on these singular supports.
-d DECIMALSExpress all output using decimal representations with DECIMALS digits.
-hPrints a help message listing the available options.
-HBy default, the program uses an enumeration method designed to visit as few supports as possible in searching for all equilibria. With this switch, the program uses a heuristic search method based on Porter, Nudelman, and Shoham (2004), which is designed to minimize the time until the first equilibrium is found. This switch only has an effect when solving strategic games.
-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.)
-qSuppresses printing of the banner at program launch.
-vSets verbose mode. In verbose mode, supports are printed on standard output with the label "candidate" as they are considered, and singular supports are identified with the label "singular." By default, no information about supports is printed.