Alex wrote:
I don't like Mike's definition "No set of voters..." because if you define the players in the game too loosely...
I reply:
I wasn't aware that a definition of "players in the game" appeared in my definition of (voting) Nash equilibrium, as we'd been using that term here.
I
Alex continued:
then not only will there be no Nash equilibrium
I Reply:
But there demonstrably are (voting) Nash equilibria, as I defined the term.
Alex continued:
, but the game itself will be ill-defined and there really won't be much to say.
I reply
About what? I didn't define a game, either ill-defined or well-defined.
I
What should there be to say, other than the definiiton, and statements about what meets the definition and what doesn't.
I and others felt that it was useful to speak of outcomes that no one could improve on, individually or collectively.
If "group strategy equilibrium" is in wide use, to mean exactly what we've been calling a voting Nash equilibrium, then I'm not saying that I object to changing to that other term. But saying that there's another word for it isn't the same as saying that the term is incorrect.
Mike Ossipoff
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