#16332: Game Theory: Build capacity to calculate Shapley value of cooperative
games.
-------------------------------------+-------------------------------------
Reporter: vinceknight | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.3
Component: game theory | Resolution:
Keywords: Game Theory, | Merged in:
Cooperative Games | Reviewers: Karl-Dieter Crisman,
Authors: James Campbell, | Travis Scrimshaw
Vince Knight | Work issues:
Report Upstream: N/A | Commit:
Branch: | e989e841387eba59b132e21ce694442af5ef26db
public/game_theory/Shapley_value_coop_games-16332| Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by kcrisman):
* status: positive_review => needs_work
Comment:
> Yay, new tag. Karl-Dieter, are you going to tell us how you do your
magic? :P
Apparently I am a Trac admin. But I'll keep the details hush-hush so as
not to abuse my new-found authority. Honestly, we probably have more
components than we need, this was pretty unusual in really not even coming
close to fitting anything else...
----
More to say:
* Earlier, you said:
> I had thought about this for a while and agree that (A,) isn't the best.
Just on this minor point, we thought about having a clean up in the init
method that would handle A, (A,) as well as (A) but require (A,B) for two
tuples etc... Is this a done thing?
So... what happened to that? I still find this syntax VERY onerous.
Economists aren't necessarily interested in typing that many commas; the
quotes are bad enough (though necessary, I think). There is a mention of
this in a test but you don't exactly take advantage of it.
* You have
{{{
A characteristic
+ function game `G = (N, v)` is superadditive if it satisfies `v(C_2)
+ \geq v(C_1)` for all `C_1 \subseteq C_2` such that `C_1 \cap C_2 =
\emptyset`.
}}}
What the heck? (This is wrong in both places.)
* In what sense is the Shapley vector fair? (Efficient, etc.) Presumably
one should mention at least briefly what criteria this is referring to.
(You do this later but not immediately.)
* Should this be set of predecessors?
{{{
where `S_{\pi}(i)` is the number of predecessors of `i` in `\pi`,
}}}
* Quite a few papers reference the computational complexity of computing
the Shapley value. I don't know whether this is worth mentioning, since
we don't implement any approximations (yet).
* ?
{{{
The Shapley value (described above) is none to be the unique
}}}
* Minor, perhaps, but should we have `symmetric` instead of `symmetry`?
----
I trust Travis that this is all implemented correctly, however (but
superadditive?) and in general I think you have something really worth
adding to Sage here!
--
Ticket URL: <http://trac.sagemath.org/ticket/16332#comment:34>
Sage <http://www.sagemath.org>
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and MATLAB
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