At this point I thought it might give more insite to
plot things by matrix. Remember that the potential liar gets one
of two matrices that are his and he doesn't share this knowledge
with the believer. He just makes a statement about which side
he is going to pick. The blues are believing and the reds are
lying. The light colors go together as the first matrix and the
darks go together as the second matrix. This was the result with
each only being able to remember the last interaction with the
other. Not all resolve at 0 and 1. In fact depending upon the
amount of information available, the graph kinds seem quite different.
I started wondering if the lie lines are independent
of each other for each matrix. I ran the stats and the answer
is a definite no. They are some strange quadratic function of
each other with statistical significance at better than 12 decimal
places. If we do one matrix at a time, essentially telling the
believer which matrix is being possibly lied about, things get
a lot more regular. But if we do them one at a time the problem
looks more like a variation on cooperation and defection, where
truth telling and believing are cooperating and lying and not
believing are defecting. Ultimately, I think I'm going to have
to conclude that this way of representing truth-telling and lying
are just the prisoner's dilemma in a different form. I think this
observation by itself might be enough for a paper, but I'd like
to go further. This result may be O.K. for we still need to look
at the problem with advice. At least now the dilemma has a moral
dimension.
Here lying is blue. This puts the two lying lines and
two believing lines together. Not too good but we wouldn't expect
that with only the ability to remember the last event. Nothing
seems to work out when we remember 2 events. So far remembering
3 events and 4 events are the smoothest and most predictable curves,
better than remembering 5 and 6 events.
This is what happens when things run a bit longer with
memory of only the last event. Hard to figure this one. A lot
of chaos when little information. Let us see if this changes with
advice.