Public goods funding…

When my paper got slashdotted, Hal Varian kindly sent me a note he had written to Bruce Schneier. It has some interesting references, but I lost it. Now I found it, and put it here so I won't lose it again.

Date: Wed, 25 Jul 2001 19:59:43 -0700
From: “Hal Varian” | This is Spam | Add to Address Book
To: [email protected]
Subject: software completion bonds

Hi. I recently looked at your article, and thought you that might like
to have a
copy of the note I sent to Bruce a few months ago.

——————–

It was a pleasure hearing you speak and meeting you in Minneapolis.

Here is the information I promised you about the “street performer
protocol”. This protocol was analyzed in the economics literature in
the context of a public goods problem. A pure public good has two
properties: 1) if I consume it, I can't exclude you from consuming it,
and 2) my consumption of it doesn't reduce the amount available to
you. Think of something like a streetlight or national defense.
Obviously, freely available information goods have essentially the
same structure.

There has been a long history of people looking for ways to “solve”
the public goods problem, and there are many clever mechanisms out
there. First, we have to define about what we mean by “solve”. The
usual idea is to design a game with a unique Nash equilibrium that
results in the public good being provided (if it is worthwhile to do
so.). [The most commonly-used solution concept for a non-cooperative
game is a Nash equilibrium: each person is making an optimal choice,
taking as given what the other player is doing.]

One mechanism (equivalent to your suggestion) is simply to have each
person make a contribution to the public good. If the sum of the
contributions exceeds the cost of production, the public good is
provided. Otherwise it is not.

Think of a simple case. A values the good at $5$ and $B$ values it at
7. It costs $10$ to produce. Since the total value exceeds the cost,
it is worthwhile providing the public good. Now if $A$ names $4$, B's
optimal response is to name $6$. Conversely, if $A$ names $6$, B will
name $4$. If $x_i$ is the contribution named by $i$, then any (x_i)$
such such that x_1 <= 5, x_2 <= 7 and x_1+x_2 = 10 is a Nash
equilibrium. So far, so good.

However, there are many other Nash equilibria. If A names 0, then an
optimal response of B is to name 0, and vice-versa. So there
are many possible equilibria of the “contribution game” that don't end
up with the public good being provided.

However, one might argue that the outcomes where the public good is
provided are particular attractvie so that you have some reason to
expect that they might be the outcome rather than one of the
inefficient equilibria. So far as I know, the first people to pursue
this research line were Mark Bagnoli and Bart Lipman. Their papers
are:

“Private Provision of Public Goods Can Be Efficient,” Bart Lipman and
Mark Bagnoli, Public Choice, 74, July 1992, 59-78.

“Provision of Public Goods: Fully Implementing the Core through
Private Contributions,” with Bart Lipman and Mark Bagnoli, Review of
Economic Studies, 56, October 1989, 583-601.

Essentially they show that the Nash equilibrium where the public good
is provided has particularly attractive properties.

(By the way, there are other solutions to the public good problem,
all of which have various drawbacks. In fact, there is a big
literature on this topic, that explores both the theory and practice
of how these decisions can be made.)

I write a monthly column for the New York Times. You
might take a look at my column of July 27, 2000,
(http://www.nytimes.com/library/financial/columns/072700econ-scene.html),
where I describe some of the economics of the Napster case, including
an allusion to the public goods mechanism analyzed by Bagnoli-Lipman.

You might also be interested in my column on liability and computer
security at:

http://www.nytimes.com/library/financial/columns/060100econ-scene.html

If you are interested, you can see other things I have written at:

http://www.sims.berkeley.edu/~hal

Again, it was a pleasure meeting you. I hope our paths cross again
some day.

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