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Dr. Martin Shubik
Coles Foundation
Yale University
New Haven, Connecticut  06520
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@greeting(Dear Martin:)

	Alas, there is less than meets the eye, anyway less than you
remember.  There are two things:

	1. In 1956 I wrote a paper, which Shannon put in the
Proceedings of the National Academy, called "Measures of the value
of information".  In this paper, I supposed that one paid a
weatherman for his advice according to the probabilities he
assigned to the different weathers and the weather that actually
occurred.  The first problem is to motivate the weatherman so that
he will tell you his actual subjective probabilities.  This puts
a certain requirement on the payoff rule.  Next we suppose that
we get payoff @i[a(i,j)] if we take action @i[i] in weather @i[j]. We also
suppose that the weatherman has experiments he can perform each
of which has a cost to him.  Now suppose we wish to motivate
the weatherman to perform the experiments that we would perform
were the decision ours with his costs for experiment and our
payoff rule.  It turns out that the solution to the problem admits
a decomposition into selling the weatherman our business and engaging
in a fair sidebet about the weather at the a priori probabilities of
the different weather before any experiments are made.

	Gleason pointed out an error in the paper that affected the
case when there were just two possible weathers, but I had lost
interest and never understood exactly what was at issue.

	2. This result suggested the more general conjecture that
when an outcome of a business is fully dependent on the actions
of a single contractor, then the only way of motivating him fully,
i.e., to make the same efforts that the owner of the business
would make, is to sell the contractor the business.  Again this
would be complicated by sidebets.  Of course, the price of the
business isn't determined by these considerations but is a matter
of bargaining.

	The problem arises when the outcome depends on the activity
of more than one person, say the owner and the contractor.  Even
if the outcome depends solely on the contractor, it may not be
possible to motivate him fully if he can't afford to buy the
business.  In these cases, one expects theorems that say that
there is no way in general that the contractor and the owner can achieve the
joint payoff that they would get if they were one person.

	What can be done depends on the extent to which the efforts
to be made by the contractor can be specified.  If they can be
fully specified and their performance verified, then there is no
problem.  The owner pays the exact costs of the efforts plus
a fixed price plus a gamble - the fixed price and the gamble
being determined by bargaining.

	The other extreme is when the owner knows nothing about
what options are available to the contractor, what their costs
are and whether he has faithfully done what he undertook.  For
example, the amount of effort may be entirely subjective.  Selling
the business will still work if the contractor can afford it.
Otherwise, various forms of contract can provide partial motivation.
My conjecture is that there should be a theory that would say
when the various common kinds of contract - fixed fee, cost plus,
payment by the hour, etc. - are appropriate and what they
accomplish.  If repeat business is possible and there are
competitors, then it should be possible to do better than
with a one shot deal.  Maybe it will be possible to prove
that in the limit, the contractor can be fully motivated.
When there are several contractors whose joint performance
is important, the problem is more difficult.

	Sociologically, it may turn out that society often works
better than the theory would predict, because people have
a desire to do what is expected of them apart from the
direct reward.  Thus we wouldn't expect a contractor to
deliberately do a sloppy job as his last job before he
retires on the grounds that he doesn't need his reputation
any more.

	Well, as you can see, it's all programmatic, and I don't
even have conjectures of precise theorems.  If any of the
people you know who are working on such problems have results,
I would like to know about it, although I have no present intention
of working in the field.

	I was so pleased to  read that you were interested in
these old ideas that I almost undertook to do some work in
the problem, but I thought better of it.  Experience has
shown that my co-efficient of return for effort outside of
computer science isn't very large.

	I hope this is helpful.
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Best Regards,




John McCarthy
Professor of Computer Science