From: Wei Dai (weidai@weidai.com)
Date: Thu Mar 13 2003 - 16:37:58 MST
On Thu, Mar 13, 2003 at 10:23:07AM -0800, Hal Finney wrote:
> That bit about everyone setting their M values at once was my invention
> to try to make concrete the idea of people choosing their M values while
> knowing what everyone else's was. Maybe a better way to accomplish it
> would be to think of repeating the funding process on a regular basis,
> say every day, where you are funding just one day's worth of public goods.
> Then the values would not change much from day to day and you'd have
> a good idea of what to expect. One paper I looked at which tried a
> lab experiment on the GL process did it that way (although with only
> 5 participants).
I saw another paper (http://www.iew.unizh.ch/wp/iewwp003.pdf) that also
repeated the experiment multiple times and saw the results converging.
But the purpose of repetition was to see if people could learn to play the
game correctly (in other words whether they could eventually figure out
that they should play the Nash strategy). The average preference for the
public good was actually given to everyone ahead of time.
It's not clear to me what would happen in a repeated game like this if the
average preference is not publicly known ahead of time. My game theory
skills are very rusty now. Not that they were that good to begin with. I
never managed to solve this repeated game with a number of periods greater
than 2: http://www.weidai.com/monopoly-memory.txt, and this game is much
simpler in that it only has two parties, and only one of them has a
preference that's not publicly known ahead of time.
> I don't think this works if we assume that no one person can wield that
> much influence. Consider a similar strategy in the private market: I
> will hold off on doing my Christmas shopping until the last day, in the
> hopes that sellers will drive their prices down due to the lack of my
> contribution to demand, then I will step in at the last minute and take
> advantage of the low prices. Well, this strategy doesn't work because one
> person's demand doesn't influence prices measurably. In the same way, my
> twiddling my knob will not appreciably influence other people's settings.
You can't carry over this intuition from the competitive market to the GL
mechanism, because the feedback mechanism in the latter operates very
differently from the former. When you turn the knob lower, that gives
incentives to everyone to turn their knobs lower, and that in turn gives
everyone incentives to turn their knobs even lower, etc., until the
effect finally dampens out. By the time it does, everyone's settings could
be significantly different from what they started out with. In contrast,
in a competitive market, when you refrain from buying and prices fall,
everyone else has an incentive to buy which drives prices back up,
so your action is mostly canceled out, instead of reinforced, by
others.
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