#18536: Solvers for constant sum games
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Reporter: ptigwe | Owner:
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-6.8
Component: game theory | Resolution:
Keywords: Game Theory, | Merged in:
Gambit, Zero-sum game Constant | Reviewers: Karl-Dieter Crisman
Sum Game, Normal Form Games | Work issues:
Authors: Tobenna P. Igwe | Commit:
Report Upstream: N/A | bb4eca8a48f9aa64a9e80a8df880d7ebb9cd20c0
Branch: | Stopgaps:
u/ptigwe/gt_extension |
Dependencies: |
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Comment (by kcrisman):
> Thanks for your comments. I've implemented most of your comments, and
noted a few extra things below which would be done upon feedback. If I've
missed anything please let me know.
Great, very quick work.
> I included it again just in case if the `_solve_gambit_LP` function was
called externally without going through `_solve_LP`. If there is no need
to retest just for this reason, then I'm happy to take it out.
Well, usually such underscore methods aren't "publicly" available. Vince,
what do you think?
> > * `return c.numpy().max() == c.numpy().min()` - is there no way to do
this without using/importing `numpy`? It would be nice to not have to use
it - or is it slower to use Sage proper?
> Currently, this compares all entries of the matrix and makes sure it is
within `sys.float_info.epsilon` of the first element.
>
||[http://git.sagemath.org/sage.git/commit/?id=d9571793d208ed772fb8e7a7a335f9934dda1fe8
d957179]||{{{Update check for constant sum 'is_constant_sum'}}}||
But which one is in principle faster or better? I don't mind using numpy
as long as importing it doesn't cause problems in speed, if it's better
(which perhaps it is).
> Currently, we are considering moving the `maximization` option into the
constructor of the class.
Fine, but this is currently breaking functionality. So either you have to
do that here, or make that change a prereq to this ticket, or something
else. My recommendation is to just leave it here for now and then deal
with the class constructor bit in a separate ticket (to make things as
orthogonal as possible).
> The LP solvers would probably be faster primarily because `lrs`
enumerates all possible extreme Nash equilibria in a game, whereas the LP
method simply finds one Nash equilibrium in the constant-sum game.
Ah.
--
Ticket URL: <http://trac.sagemath.org/ticket/18536#comment:8>
Sage <http://www.sagemath.org>
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