Comment author:cousin_it
26 October 2010 08:55:36AM
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12 points
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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.

## Comments (28)

Best*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.

the link is broken

Interesting.