Re: poly: No expected value colonization equilibrium?

At 11:55 AM 12/15/97 -0800, you wrote:
>Carl F. writes:

>This case of exponential decay was the case I was considering.
>Sorry to have not been clear. Under exponential decay,
>my rate of decay per unit distance is unaffected by whether I stop and
>colonize now. That's what drives the result.

Whoops, you're right.

I think we can agree that a model which predicts that the optimal strategy
is to send probes to an infinite distance with zero probability of survival
is not a good model.

Your suggestion of non-exponential attrition is a good one. If probes fly
in single file, far enough apart, an impact will only destroy the lead
probe. In this model, attrition is linear.

Here are two other things we haven't taken into account.

It may be possible for probes to tell which of the oases ahead of them have
already been colonized, by observing signals sent out either accidentally
or deliberately by the colonizers. (Imagine a neon sign a billion
kilometers long, brighter than a thousand suns, that says "Private
property, keep off". (A sign has to be big to indicate that it's not a
bluff)) In this case, the probes can aim for oases that appear to be
unoccupied.

By communicating among themselves, a fleet of probes may be able to monitor
their own attrition. So far we've been assuming that probes need to decide
on where to stop without knowing the state of any other probes. If this is
not true, the best thing to do might be to change strategy depending on the
number of surviving probes.

Alas, I don't have time to work out the implications of these effects right
now.

--CarlF

  
Received on Tue Dec 16 15:59:15 1997