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QuantEcon / GameTheory.jl

Algorithms and data structures for game theory in Julia
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Extend support enumeration to N-player games #47

Open oyamad opened 6 years ago

oyamad commented 6 years ago

By using a nonlinear equation/complementarity problem solver or a polynomial equation solver (if any).

What packages are available in Julia (and in Python)?

oyamad commented 6 years ago

Well-known polynomial equation solvers (not in Julia):

Some discussion: https://groups.google.com/forum/?fromgroups=#!topic/julia-users/HTbw39F0ejc

oyamad commented 6 years ago

Are these applicable?

blegat commented 6 years ago

The plan is to make SemialgebraicSets.jl independent on the algorithm/library used a bit like Polyhedra.jl. In Polyhedra, you build your polyhedron with polyhedron(::HRepresentation, ::somelibrary). In SemialgebraicSets, you will do algebraicset(::Vector{<:AbstractPolynomial}, ::somelibrary). There is a solver implemented in pure Julia in SemialgebraicSets but we are planning to also make HomotopyContinuation an option. There is also this solver: https://github.com/wbhart/Singular.jl which works in exact arithmetic. Ideally it would be nice if it could be used from the algebraicset function. We could even make it so that the default library if the polynomials are Nemo polynomials then the default library is Singular.

It would of course also be nice to add wrappers to C/C++ libraries like Bertini to be used through the same interface :-P

oyamad commented 6 years ago

@blegat Thanks. Sounds great!

oyamad commented 1 year ago

https://github.com/QuantEcon/GameTheory.jl/pull/174#issuecomment-1367809331