Forest had correctly said:
Under winning votes the C faction can take defensive action and
truncate to 20 C. The resulting position is a Nash Equilibrium.
Chris writes:
Taking such "defensive action" causes B to win, so why would they want to do
that when they
prefer A to B? And I don't see why the resulting position is a "Nash
Equilibrium"
(according to
the definition I googled up), because the sincere C>A faction can change the
winner from B to A
by changing their votes from C to C>A.
I reply:
The Nash equilibrium isnt one in which the offensive order-reversal takes
place. In the Nash equilibrium, the C voters truncate, and the would-be
order-reversers dont order-reverse. The B voters wouldnt benefit by
changing their vote, and the would-be order-reversers would suffer if they
order-reversed. Thats the Nash equilibrium. The B voters, by truncating,
make the would-be reversers accept the Nash equilibrium or suffer the
consequences.
Mike Ossipoff
DEFINITION: Nash Equilibrium If there is a set of strategies with the
property that no player
can benefit by changing her strategy while the other players keep their
strategies unchanged, then
that set of strategies and the corresponding payoffs constitute the Nash
Equilibrium.
http://william-king.www.drexel.edu/top/eco/game/nash.html
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