From: Robin Hanson <hanson@econ.berkeley.edu>

Date: Mon Dec 15 1997 - 11:55:38 PST

Date: Mon Dec 15 1997 - 11:55:38 PST

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

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