#16954: Game Theory: Build class for normal form games as well as ability to
obtain
Nash equilibria
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Reporter: vinceknight | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: game theory | Resolution:
Keywords: Game Theory, | Merged in:
Normal Form Games | Reviewers: Karl-Dieter Crisman
Authors: Vince Knight, | Work issues:
James Campbell | Commit:
Report Upstream: N/A | c7e42b7618ee46f81443b626b4fc3b5aa8fb095a
Branch: | Stopgaps:
u/vinceknight/fixing_bug |
Dependencies: |
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Comment (by vinceknight):
Replying to [comment:36 kcrisman]:
> > As I said above I think you have actually found a bug in the algorithm
here. My hunch is that it's something to do with pruning so will take a
look at that: your examples are going to serve as tests and will be
incorporated in. **Thank you very much for spotting this.**
>
> You're very welcome; I really have a lot of motivation to encouraging
more people in voting/choice/strategy to start using a standard tool.
>
> Also, I should point out that there are three sorts of things I noticed
with this.
> * Places where it was degenerate and `'enumeration'` didn't give as
many pure equilibria (in one case, none). Perhaps this is a bug in
enumeration, as you say.
I have addressed this: it was a genuine bug where we were trying to be
quick (which worked for non degenerate games) but we were in effect
incorrect. Have added tests as well.
> * The fact that a certain type of degenerate case is very easy to
recognize from the form of the matrices and could conceivably be checked
for. That is probably a followup ticket.
I would prefer to have this as a follow up ticket (but can already start
lining up a student to work on it!).
> * One example where it was possibly degenerate but where `'lrs'`
''inside of Sage'' gave a pure strategy which is not a NE, and which is
''not'' returned by the LSE online lrs service (which does return all the
pure strategies `'enumeration'` does in this case). So perhaps we are
using lrs incorrectly.
This was also a bug but this time a bit more of a clumsy one. Our parser
was assuming a certain format. This has been fixed now (more tests added).
>
> I'll wait to review the other changes until you have this and the tuple
thing sorted out, though I'm not worried about them :)
I have also addressed the tuples/vectors issue. I've gone with tuples and
also sorted the output of both algorithms so this way the algorithms do
give the same output (even taking ordering in to account).
I am afraid though that I don't seem to have the PIPE doc build locally.
Am I looking in the wrong place? I ran `./sage -b; ./sage -docbuild
reference/game_theory html` (Note that I had to run a `make doc-clean`)
with no problems and when I go to
`src/doc/output/html/en/reference/game_theory/sage/game_theory` I only
have two html files: 'cooperative_game.html' and 'normal_form_game.html'.
If I'm looking in the wrong please please let me know...
--
Ticket URL: <http://trac.sagemath.org/ticket/16954#comment:43>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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