Game theory

Stream: maths

[Sahil Sharma]

Can someone give an estimate on how much of game theory has been formalized?

[Violeta Hernández]

Game theory means at least two things in math

[Violeta Hernández]

Are you thinking Nash, or Conway?

[Sahil Sharma]

I am aware of the work done in combinatorial game theory formalization, I was thinking of Nash.

[Violeta Hernández]

Oh, that I know nothing about :frown:

[Sahil Sharma]

Oh, just in combinatorial game theory, could you give me an estimate of how far is it done?

[Violeta Hernández]

We have a lot of the basic theory of game comparison nailed down, we have Sprague-Grundy for impartial games, and I believe @Scott Morrison did something with small games and Domineering

[Violeta Hernández]

Surreals are still quite underdeveloped, and we don't even have surreal multiplication yet, though @Junyan Xu and I have been working on that

[Violeta Hernández]

That's about it

[Sahil Sharma]

Thanks a lot, I was looking for an answer like this :smile: , I am still curious to know if something has been done on Nash side of things, regardless thanks for your answer.

[Yaël Dillies]

I am currently doing some convex analysis which is tangential to Nash's stuff. @Apurva Nakade is another good person to ask about.

[Yury G. Kudryashov]

Are you going to prove either of the relevant fixed point theorems?

[Yury G. Kudryashov]

I mean, Kakutani and Brouwer fixed point theorems.

[Yaël Dillies]

Yes, this is what branch#sperner-again is about.

[Apurva Nakade]

Hi, I'm currently working on formalising Farkas' lemma (Section 2.3 here). This is mostly analytic and I don't think it'll intersect game theory.