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• CommentRowNumber1.
• CommentAuthorjulesh
• CommentTimeJul 9th 2019

In the spirit of yesterday’s discussion about applied topics on the nLab, I have begun creating an article for game theory. The page previously existed just as a list of references, but there doesn’t seem to be an nForum thread about it.

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeJul 9th 2019

Just a note about editing: the best way to make an announcement about changes to a page is to enter them in the “changes” text box below the edit area when you save the page. Then an nForum discussion thread will be automatically created, if it doesn’t exist already, and will be named so that future edit announcements will automatically go to the same thread and the “Discuss this page” link at the top of the page will go to that thread as well.

• CommentRowNumber3.
• CommentAuthorjulesh
• CommentTimeJul 9th 2019

Got it, thanks

• CommentRowNumber4.
• CommentAuthorjulesh
• CommentTimeJul 10th 2019

• CommentRowNumber5.
• CommentAuthorGuest
• CommentTimeJul 13th 2019
This seems utterly superficial. Other than sharing the word "homotopy" I don't see any connection. I would rather the nlab not be filled with wild speculation since it is already struggling to back many claims it is making. Perhaps I am being an old hermit, but I have yet to see what "applications" applied category theory has other than saying things we know in an obfuscated way.
• CommentRowNumber6.
• CommentAuthorMike Shulman
• CommentTimeJul 13th 2019

While I disagree with the overall opinion expressed in #5 (and especially the tone), in this particular case I do think that the connection to homotopy theory seems rather remote. I had a glance at the paper in question, and by the “homotopy method” it seems to refer to an essentially analytic/topological method for finding zeros or fixed points applied to examples in game theory, with practically nothing at all to do with what we call “homotopy theory”. What do you think, Jules: is there some deeper connection there that we’re missing?

• CommentRowNumber7.
• CommentAuthorTodd_Trimble
• CommentTimeJul 13th 2019

I also find the second half of #5 overstated, but I would add to the first half that self-assessing one’s speculations as “good and solid” is almost always unconvincing for anyone else, and is likely to backfire.

• CommentRowNumber8.
• CommentAuthorMarc
• CommentTimeJul 15th 2019

The link to the Cockett et. al. paper threw an error, so I changed it and also completed the author list

• CommentRowNumber9.
• CommentAuthorRichard Williamson
• CommentTimeJul 15th 2019
• (edited Jul 15th 2019)

I think “good solid” was probably not intended seriously, i.e. was probably intended to be similar to “good old” :-).

The “since” in the third sentence of #5 seems to be something of a non sequitur!

• CommentRowNumber10.
• CommentAuthorTodd_Trimble
• CommentTimeJul 16th 2019

Re #9: is that a thing? I’d never heard “good solid” as an expression.

• CommentRowNumber11.
• CommentAuthorDavidRoberts
• CommentTimeJul 16th 2019

Regarding the ’homotopies’ of Herings and Peeters mentioned (in at least v5), I haven’t looked at the paper (in the journal Economic Theory), but I can imagine the authors just using topology, and jazzing up the name because one is moving continuously through a space of strategies, hence continuously deforming the strategy, which sounds like homotopy to the untrained ear.

• CommentRowNumber12.
• CommentAuthorDavidRoberts
• CommentTimeJul 16th 2019

Looking at the paper, the authors use a result of Browder about fixed points of maps $[0,1] \times S\to S$ for compact convex $S\subset \mathbb{R}$. Looks more like straight-up topology together with optimisation algorithms to me.

• CommentRowNumber13.
• CommentAuthorMike Shulman
• CommentTimeJul 16th 2019

Okay, sounds like the speculation is not actually good or solid. (-: Is it worth retaining any mention of this paper on the page, or should we just delete the entire section?