#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 | 8775f12e2644129b2a790ad91f37b853a273d2b6
Branch: | Stopgaps:
u/vinceknight/mainly_fixes_to_docs |
Dependencies: |
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Comment (by 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.
* 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.
* 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.
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 :)
--
Ticket URL: <http://trac.sagemath.org/ticket/16954#comment:36>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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