From: Hal Finney (hal@finney.org)
Date: Thu Mar 13 2003 - 11:23:07 MST
Wei writes:
> In the paper, the decision is just one-shot, without this dynamic
> feedback process. Everyone is assumed to already know the average M
> before the whole things starts. One might ask what's the purpose of
> the mechanism then, if everyone already knows the outcome? Apparently
> the implicit assumption is that everyone knows except the government,
> and the government needs this mechanism to find out the answer. If my
> interpretation is correct, this seems to make the Groves-Ledyard mechanism
> useless in real world situations, where the real average M is unknown,
> because people would be taxed less on how much their preferences differ
> from the average, and more on their ability to guess the correct average.
> This seems to be rather unjust and unlikely to be widely adopted. It
> also means that you can't just ignore the public goods that you're not
> interested in. You have to become an expert in every one so that you
> can guess the correct average preference.
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).
Generally the GL analysis assumes that there are enough people that no one
person can influence the prices. This is in keeping with the flavor of
"neo-classical" economic analysis of private markets. People are assumed
to be "price takers", meaning that we accept prices as given and don't
expect our decisions to alter prices except to an infinitisimal degree.
That's how most of our shopping is done, and it is the same kind of
assumption being used in the GL government.
Setting M values is analogous to setting prices in a private market.
It is generally assumed you know what other people are asking and
offering when you make your own bids. This seemingly leads to an infinite
recurrence, where no one can bid until they know what others are bidding,
but in practice it is resolved easily. I think the same thing can be
true of the GL mechanism.
> In your dynamic scheme, things don't quite work because everyone has
> an incentive to lie until right before the end. Suppose you have a
> greater than average preference for the public good. You would want to
> turn your dial as high as possible to create the impression that the
> average preference is higher than it really is. This gives an incentive
> to everyone else to turn their dials higher (closer to the average) to
> reduce the "non-conformity tax". You can then switch back to a lower
> setting one second before the vote ends. If everyone knows this, of
> course, they'll just disregard any display of the current average and
> this scheme becomes equivalent to the original one-shot scheme.
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.
AS GL write (page 807): "Just as in a finite agent Arrow-Debreu
economy [i.e. a private-goods economy] a sophisticated consumer can
gain by considering how prices and his profit shares are affected
by his own demand; in our public goods model, under our mechanism, a
sophisticated consumer can gain by considering how equilibrium prices,
his profit shares, and the other consumers' messages are affected by
his own decisions." Earlier on that page they write: "our competitive
assumptions imply Nash equilibrium decisions are chosen." They are
rejecting more elaborate game theory strategies such as you propose
and focussing on Nash equilibria. In the context of a large market and
competitive (i.e. non-cooperative, non-colluding) behavior, that is a
reasonable assumption.
Hal
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