Re: poly: No expected value colonization equilibrium?

Carl F. writes:
>At 11:50 AM 12/12/97 -0800, Robin Hanson wrote:
>>I've been trying to apply game theory to the colonization
>>situation Carl F. raised, and I seem to have proven that
>>conclusion that there is no colonization equilibrium when
>>probes only care about the expected value of the number of
>>descendant probes they produce at each point in space time.
>
>If probes can continue indefinitely with no risk, then this is the correct
>conclusion. However, consider the case where probes have a certain
>probability per unit time of being lost. ....
>Under the assumption that the main mortatilty to probes is caused by random
>uniformly distributed events such as collisions with dust grains, -
>d(ln(A))/dt is a positive constant,

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.

I now think a better model must explicitly look at the likely possibility
that decay is probably stronger than exponential. Big objects in the
path give a constant probability of destruction, but small objects
probably accumulate their damage.

>In this case, what we are
>interested in maximizing is the probability of the proble surviving to time
>t, multiplied by the probability of finding an unoccupied oasis at that
>time.

My analysis applied to a much wider range of possible probe goals.

Robin Hanson
hanson@econ.berkeley.edu http://hanson.berkeley.edu/
RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884
140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-8614
Received on Mon Dec 15 19:49:31 1997