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.
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.
the link is broken
You can plug it into the Wayback Machine.
thanks, it worked! https://web.archive.org/web/20150412211654/http://reducing-suffering.org/wp-content/uploads/2015/02/wild-animals_2015-02-28.pdf
Interesting.