[EM] Steve: Nash Equilibrium

MIKE OSSIPOFF nkklrp at hotmail.com
Mon Nov 22 06:56:35 PST 2004

I had said:

>>As we on EM have been using the term for voting systems, a Nash 
>>equilibrium is an outcome, and the votes
>>configuration that caused it, that no set of voters can improve on for 
>>themselves by voting differently.

Mike's definition here is incorrect.  He gave the
definition for a "group strategy equilibrium."
Those equilibria are rarer than Nash equilibria,
which merely require that no _individual_ voter
can get an outcome she prefers more by changing
her vote (holding all the other votes constant).

  I reply:

  Did I say that the definition that I posted was the one written by Nash, 
or did I say that it was
the way that we've been using the term on EM? My statement that you quoted 
above was correct: The term had been, for some time, in accepted use on EM 
with the meaning that I gave.

And it's also been clarified here that when we here say "Nash equilibrium", 
that's short for "voting Nash equilibrium".

If you mean that "Group Strategy Equilibrium" is a term in wide use 
elsewhere for what we here have been calling a voting Nash equilibrium, then 
thanks for informing us that there's another term.
  But it certainly doesn't mean that "voting Nash equilibrium" is incorrect.

I'd suggest that the terminology isn't the important thing, provided that 
the terms we use have been defined.

Mike Ossipoff

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