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cousin_it comments on Let's split the cake, lengthwise, upwise and slantwise - Less Wrong

43 Post author: Stuart_Armstrong 25 October 2010 01:15PM

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Comment author: cousin_it 26 October 2010 08:55:36AM *  12 points [-]

I just spent five minutes on a fun little math problem lurking in your post. The Nash solution uses a family of hyperbolas, so it's natural to ask the question: what other curves could be used instead? In other words, which families of curves are invariant under scalings in x and y? Turns out it's easy to prove (try it!) that all such families have the form x^a*y^b=c, where a and b are constant but c varies. These are the "generalized Nash solutions" where the players have unequal "bargaining powers". For further reading see this PDF.

Comment author: MathieuRoy 27 January 2018 09:48:24AM 0 points [-]

the link is broken

Comment author: Stuart_Armstrong 26 October 2010 05:31:07PM 0 points [-]

Interesting.