PolEnumSolve

Name

PolEnumSolve -- Computes Nash equilibria by enumerating solutions to polynomial equations

Synopsis

PolEnumSolve[support->NFSUPPORT, {stopAfter->0}, {nEvals<->0}, 
             {time<->0.000000}, {traceFile<->(Output)}, {traceLevel->0}, 
             {singularSupps<->{  }}, {recurse->True}] =: LIST(MIXED)
PolEnumSolve[support->EFSUPPORT, {asNfg->False}, {stopAfter->0}, 
             {nEvals<->0}, {time<->0.000000}, {traceFile<->(Output)}, 
             {traceLevel->0}, {singularSupps<->{  }}, 
             {recurse->True}] =: LIST(BEHAV)

Description

PolEnumSolve solves for all totally mixed Nash equilibrium on support. If recurse is True, the algorithm iterates through all sub-supports of support to find the full support equilibria on each sub-support. Supports with singular solutions are reported in singularSupps. These supports are skipped by the algorithm when determined to have singular solutions.

On each sub-support, the algorithm starts with a cube containing the space of possible solutions and proceeds recursively. The recursion step begins with a subcube. The subcube is discarded if the cube is irrelevant in the sense of lying outside the space of possible solutions. Otherwise a modified Newton's method is used to search for a solution in the subcube. In the event that such a solution is found, Taylor's series information at the solution is used to inquire whether the solution is necessarily the unique solution in the subcube. If Newton's method leaves the subcube before finding a solution, Taylor's series information at the center is used to inquire whether we can be sure that the subcube contains no solutions. If neither of these procedures resolves the issue, the subcube is subdivided and this recursion is performed on each smaller subcube.

The following optional parameters may be used to modify the behavior of the algorithm:

See also

PossibleNashSupports.