
We Can’t Have Efficiency, Good Incentives and No Deficit - chritchens
https://medium.com/@Chritchen/we-cant-have-efficiency-good-incentives-and-no-deficit-2fa0882d08f7
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kortilla
Note to potential readers: this doesn’t apply to governments even though the
title hints at it.

This is about a very constrained economic game with hidden information.

~~~
chritchens
Goverments are very complex things. It can apply to single policies. Then here
we go into politics, and I don't care to.

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drdeca
I am guessing that by \Theta , the author means the product of the \Theta_i ?

In the third paragraph, they say it is the “set of type profiles of all the
agents”, which seems to suggest maybe {\Theta_i | i in U}, or maybe the
disjoint union of the \Theta_i , but for the social choice function being from
\Theta to X to make any sense to me, \Theta has to be the product of the
\Theta_i over i in U. So I assume this is what is meant.

The author also writes that M is “the set of all message spaces”, which seems
to mean { M_i | i in U }, but again, I cannot make sense of that with regards
to the decision rule \varphi having it as the domain. So, I also assume that M
is actually meant to be the product of the M_i (with i ranging over U).

It seems strange that the cost-sharing mechanism is defined as being a
function only of the agent index? It seems like the term “mechanism” should
mean that it includes how the cost imposed on each agent is determined, not
just, be the result of what cost is imposed on each agent?

I’m confused about the example. Are the different agents making offers
sequentially?

I don’t think the author clearly established (or, really, even clearly stated)
their claim.

They define a bunch of terms (like \Theta , M, \varphi ) but then they don’t
do anything with them, or really say much of anything about them after they
defined them.

They might have something interesting they are trying to say, but I don’t
think they make it clear.

The second source it cites ( at
[https://crypto.stanford.edu/portia/papers/mukind-
thesis.pdf](https://crypto.stanford.edu/portia/papers/mukind-thesis.pdf) )
looks interesting though, and I think is where they got the thing they were
trying to explain (though it is much longer!).

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chritchens
sorry for the late reply drdeca, technical problem. Have still to parse your
reply. I will try to give you a response anyway.

1) Well, there is no product of \Theta_i, it's sets. It's the set of all the
\Theta_i.

2) the article is sequential, so it's {\Theta_i | i in U}.

3) M is the set of all the possible messages that can be sent by the agents,
not the actual messages sent. That's why it's message _space_.

4) the cost mechanism depends on the service itself, that's why its shape is
know beforehand. If you have to allocate M&Ms, you know the cost of any unit,
the logistic costs (let's say an average or a worse case scenario), etc.

5) nothing is implied on the order of the message submissions.

6) I don't think so, but you are the reader. I'm taking feedbacks to improve
in the next articles. One was to add images and diagrams. The claim is just
that we cannot have efficiency, incentive-compatibility and no deficits cause
we cannot have prices that act perfectly both as a way to recover costs and a
way to incentivize agents.

7) fair. At start I wanted it to be longer, and then I understood that a) it
was taunting to read somehow b) I had to split it. It's the first of a series.
Worst case scenario I will link to this first article in the next ones.
Tradeoffs maybe. I wanted to be correct, not just to describe the problem.

8) point 6.

9) from the first source I've taken the general description of mechanism
design, and the second was the best I found on the problem. To be honest, the
second constrained me to choose the first. And the first and some lectures
from Bonn university (Germany) were the best I've found so far.

Happy to answer to further questions, and, again, apologies for the late
reply.

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SimpleSimonSays
Cannot recommend.

I've seriously tried to read this and the notation is mathematical but poorly
used and the whole article has no conclusion or point but serves to introduce
another article.

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drdeca
At first I thought you just meant that they used mathematical notation when it
wasn’t helpful, but when I actually read it, I realized what you meant by
“poorly”, and I agree with you.

I might say that they _tried_ to use mathematical notation.

~~~
chritchens
Look at the reply I gave to the user you replied to. I listed the parts of the
sources I used. I found really difficult to find a unified notation, but
that's the sense. Try to read the parts I listed, and check if it's more
understandable to you.

Apologies for the late reply. Technical problems.

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soVeryTired
Sounds a bit like Arrow's impossibility theorem, which I see as an exercise in
how to sneak unreasonable constraints into a reasonable-sounding problem
formulation.

~~~
chritchens
Complex. Too long to discuss here. Politics then. Not helpful. Thank you for
citing the theorem though.

