#16954: Game Theory: Build class for normal form games as well as ability to
obtain
Nash equilibria
-------------------------------------+-------------------------------------
Reporter: vinceknight | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: game theory | Resolution:
Keywords: Game Theory, | Merged in:
Normal Form Games | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | ffa6d525b5e6681687642d9efc80037884823e30
u/vinceknight/16954 | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Comment (by kcrisman):
Before continuing, I just have to say that this is really exceptionally
well-organized. Good work.
----
Moving on to the methods.
* But what will happen to the deleted game? Will this raise an error if
you try to do anything with it? (Maybe I'll find out later.)
{{{
sage: prisoners_dilemma
{(1, 0): [0, 5], (0, 0): [2, 2], (1, 1): [4, 4]}
}}}
* Can you {{{__setitem__}}} for an already-set item in the game? If not
(for whatever reason), then this should be doctested. If yes, I guess
this should be justified and doctested too.
* Can you move that method to with the other dictionary-emulating
methods? Not super-important but helpful to those reading code.
{{{__iter__}}} and {{{__len__}}} strictly speaking are not about dict
emulation but just emulation of iterables.
* Usually {{{__init__}}} is best at the very first. Am I missing
something that the emulation ones are coming first?
* I would have expected this to list the bimatrix entries. Instead I get
a very boring list of the possible pure strategies.
{{{
sage: for key in prisoners_dilemma:
....: print key
}}}
Will length basically always be n times m in terms of the number of
strategies? In which case do you really need all that extra stuff about
utilities?
* `Generator function must be a list or nothing` is not doctested.
* `generator != None` or `generator is not None`? Just wondering which
you intend here.
* ` LaTeX method shows nothing interesting for games with more
players::` - then you should probably use the `...` like so:
{{{
\text{\texttt{<bound{ }method{ }NormalFormGame...[False,{ }False,{
}False]{\char`\}}>}}
}}}
or the like.
* I still do not like ` return str(self.utilities)` for the string rep.
It should at least say, at the very least, that it is in fact a normal
form game!!! Maybe "Normal Form Game with following utilities" or
whatever.
* One of the errors in the payoff matrices method is tested, the other
isn't.
* `m1 = matrix(QQ,` - oh, oh. But didn't you say that Gambit does
floats? And what if people input floats? I'm just thinking of nasty
things like people inputting `1/sqrt(2)` as a probability, or ones where
when they are coerced to rationals don't add up to 100%
* I'd like to see an example with
{{{
sage: g._generate_utilities(True)
}}}
where it would actually destroy a utility. Myuh-ha-ha!
* The line
{{{
Checks if ``utilities`` has been completed
}}}
doesn't seem to correspond to any errors, though.
* These mixed strategies
{{{
[[(1, 0, 0, 0), (127/1212, 115/1212, 485/606)], [(0, 1, 0, 0), (0, 1/26,
25/26)]]
}}}
seem strange, but I assume correct - can you confirm they are ''exact''
answers?
* The line
{{{
This particular game has 3 Nash equilibria::
}}}
isn't backed up by
{{{
sage: g.obtain_Nash(maximization=False)
[[(1, 0, 0), (0, 1)]]
}}}
unless I'm misunderstanding the syntax. Where are the other two
equilibria promised to the reader? This seems to happen in a few other
examples. (Actually, I think that some copy-paste is at fault here, esp.
since `maximization=False` but that isn't mentioned.)
* The or a?
{{{
A function to return the Nash equilibrium for a game.
}}}
* When you use `tmp_filename()` in the things themselves (not doctests)
are there any other strange side-effects?
* I feel like you tired (understandable!) in the `_solve_enumeration`
doctests. Most of them should be tests and not examples in any case, I
suppose. Here is the funniest of them, I actually laughed at this one.
{{{
TESTS:
Due to the nature of the linear equations solved in this algorithm
some negative vectors can be returned. Here is a test that ensures
this doesn't happen::
sage: a = matrix([[-13, 59],
....: [27, 86]])
sage: b = matrix([[14, 6],
....: [58, -14]])
sage: c = NormalFormGame([a, b])
}}}
It sure doesn't happen! Since we never try to find said vectors :-)
* Adding strategies should then have an example finishing it.
{{{
If we do this and try and obtain the Nash equilibrium or view the
payoff
matrices(without specifying the utilities), an error is returned::
}}}
but it's never finished up.
* What happens with a completely trivial matrix i.e. all payoffs are
zero? Then all mixed strategies are optimal, I guess...
----
Remaining:
* Making sure the `_solve_enumeration` actually is correct. I'm sure it
is, I just haven't had time to look at it.
* I will have to just trust you on the `_Hrepresentation` method.
Almost there!
Finally, as a general rule of thumb, if you have any pretty useful tests
or examples which are in underscore methods (which won't show up in the
reference manual) maybe repeat them elsewhere. I don't know if you do
that, just mentioning it.
--
Ticket URL: <http://trac.sagemath.org/ticket/16954#comment:15>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
