From: Benja Fallenstein (email@example.com)
Date: Wed May 20 2009 - 10:24:44 MDT
On Wed, May 20, 2009 at 5:50 PM, Matt Mahoney <firstname.lastname@example.org> wrote:
> --- On Wed, 5/20/09, Stuart Armstrong <email@example.com> wrote:
>> Option A gives you (1/2)^n each day forever, where n is the day.
>> Option B gives you the option of claiming, on any day n, the payoff of
>> option A from say 0 up to day 2n, say. (this gives a pay off of 2 -
Yep, that would've been my answer too.
> We wish to test two hypotheses about an agent.
> H1: the agent believes itself to be immortal. It puts equal value on A and B.
> H2: the agent believes that with probability 1/G that it will die at time G, otherwise it is immortal, where G is [an arbitrarily large] number. The agent places a very slightly higher value on option B.
It's a question of definition, but IMO the agent should place higher
value on A under H1; in this case, it can get a payoff arbitrarily
close to one from B, but it cannot actually get a payoff of one. To
put it differently, the agent should evaluate the expected payoff of
all possible strategies it can adopt over its whole lifetime, and then
execute one of the strategies with the highest expected payoff (if
there is one -- not a given if there are an infinite number of
possible strategies, but in this case there is). In the scenario
Stuart presented, under your H1, choosing A on day one has a higher
expected payoff than any strategy involving choosing B.
All the best,
- Benja (with an 'a', btw :))
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