#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: Karl-Dieter Crisman
Authors: Vince Knight, | Work issues:
James Campbell | Commit:
Report Upstream: N/A | 9e14ff21121029f311b53d608b6a6d826ff2af88
Branch: | Stopgaps:
u/vinceknight/finishedresponsetobigreview|
Dependencies: |
-------------------------------------+-------------------------------------
Comment (by kcrisman):
Okay, back to the algorithm. Here was one thing I definitely was confused
by before.
> Equivalently we can consider consecutive rows of A (instead of all pairs
of strategies).
Huh? I distinctly remember that part of the code, but I don't see it in
the references. So maybe this is just some very basic linear systems
thing I am not remembering, but if you can clear it up for me I'd be
grateful.
Along these lines, you then need to change
{{{
where `A` has been modified to only contain the row corresponding to
`S(\rho_1)`
}}}
to
{{{
where `A` has been modified to only contain the rows corresponding to
`S(\rho_1)`)
}}}
(since there is a necessary parenthesis (oh, WHY do the Brits call them
brackets when brackets are square? (truly, I don't know))).
> > > * Minor but made the code harder to understand:
> > Have tried to clarify as suggested: let me know if it still isn't
quite right.
> Hmm, I kind of meant the opposite - shouldn't `j` be a `p1_strategy` and
so forth? Perhaps I'm misunderstanding this. For stuff like this,
variable names that mean something are crucial. Plus, the new code still
mixes letters and `strategy`s.
Oh, ''now'' I get it (thanks to your improved exposition and CUP's kind
provision of [http://blog.oddhead.com/2007/09/17/computational-aspects-of-
prediction-markets-book-chapter-and-extended-bibliography/ a free download
of AGT]). These are maybe to distinguish between using ''all'' strategies
and just the ones in the truncated list of ones in the support?
Or if not, then I stick with my original request.
By the way, you can just move the comments like this
{{{
# Coefficients of linear system that ensure indifference between two
consecutive strategies of the support of p1
}}}
to the line immediately preceding, to ensure good readability.
I note that in the built doc for some reason there is documentation for
`sage.game_theory.normal_form_game.PIPE`. I couldn't tell you how to
remove it but it does seem odd.
----
So now one can move to the testing phase!
--
Ticket URL: <http://trac.sagemath.org/ticket/16954#comment:27>
Sage <http://www.sagemath.org>
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