#16331: Game Theory: Build capacity to solve matching games in to Sage.
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Reporter: vinceknight | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: game theory | Resolution:
Keywords: Game Theory, | Merged in:
Matching Games, | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | 31fc55432bfc19381d2d09e5602e7bfe5c496f6c
u/vinceknight/game_theory__build_capacity_to_solve_matching_games_in_to_sage_|
Stopgaps:
Dependencies: |
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Comment (by vinceknight):
Replying to [comment:45 kcrisman]:
> Comments I could reconstruct:
> * Should it be a game of 2n players or size n? Is there a standard
terminology?
> * Since the matching $M$ is bijective and the algorithm is not
symmetric, should the solution really have each match twice?
> {{{
> sage: m.solve()
> {'A': ['J'],
> 'C': ['K'],
> 'B': ['M'],
> 'D': ['L'],
> 'K': ['C'],
> 'J': ['A'],
> 'M': ['B'],
> 'L': ['D']}
> }}}
> maybe instead
> {{{
> sage: m.solve()
> {'A': ['J'],
> 'C': ['K'],
> 'B': ['M'],
> 'D': ['L'],
> }}}
> and then it will be easy to tell if it's inverted...
> * `_repr_` really shouldn't have it possible to have something other
than $2n$. I'm not asking to check the `_is_complete` at that point, but
at least they should be same number can be checked.
> * `latex` - I'm not sure this is standard notation. `4=\{(1, 0)\}`
equals sign?
> * in `game_to_dict` I just don't know whether one should have
"undicted" the game in the first place. It seems like a lot of trouble to
redictify the game. Maybe the data should be stored differently in any
event. Constructing a whole `_Player` for each player seems like a lot of
overhead. They have no external existence.
> * Is it possible for someone to access all the partners and pref and
such in such a way as to mess with `_is_solved`? It just seems odd that
those things might be directly accessible.
> * I think another word than 'complete' is needed in checking
completeness, because if `{3: (0, 2, 1)` was changed to `{3: (0, 2)` it
would still raise the error but seem "complete" in some sense...
> * What if the automatically added suitor name is already in use? (Say,
we already have names `3, 'Fred'` and now want to automatically add a
third one.) I don't know the right answer here.
> * Any rationale for the autoprefs?
> * I wonder if `sol_dict` should be an attribute and not a method.
Especially since you're not really supposed to access it publicly.
> * And of course, if you REALLY want to use the `_Player` class, needs
doctests :)
Thanks Karl, will read through these carefully and work on them sometime
this week.
--
Ticket URL: <http://trac.sagemath.org/ticket/16331#comment:46>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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