I don't know the answer to the problem as you stated
it.  I did, however, recently work for a state Senate
campaign and asked alot of questions.  One thing they
told me was that negative advertising only puts doubt
in the mind of the unaligned voters regarding the
opponent rather than winning any voter's support.

As an example, here in Michigan, Dick Posthumus was
trailing Jennifer Granholm in the polls by quite a
bit.  The Posthumus campaign ran no positive Posthumus
ads for quite some time, instead running negative ads
about Granholm in the hopes of getting unaligned
voters to abandon her.  Once the polls showed that
alot of unaligned voters had become undecided again,
the Posthumus campaign started in on the positive
Posthumus ads to win those undecided voters over.  In
the end the results were close.

I know that doesn't help solve the problem as you
worded it, but perhaps the payoffs are different from
what your example assumed.  So any candidate trailing
in the polls will run negative ads to make the
unaligned voters become undecided again.  Once that is
accomplished, all candidates must begin competition
all over again for those votes.  With three viable
candidates, I suppose the two trailing ones must play
a game of brinkmanship, waiting for the other to go
negative, and cash in on the newly dislodged voters.

-jsh

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