Ch. 5: Summary
Aaron Swartz
I'd just summarize this chapter for you (as I'm also doing with
Keynes' _General Theory_ on my blog this week). If you did read it,
feel free to help fill in the gaps.
Our two fishers from before have figured out how to work together so
that both are better off; now they're trying to decide how to split
the resulting fish. Obviously neither will accept less than they had
before, but it's not obvious where to meet in between. This is a
_bargaining problem_. (Tautologically, how much someone gets in a
bargain is their _bargaining power_.) Some say distribution is
politics, not economics; Bowles thinks they can't be separated.
There's not a single coherent model of bargaining, so we'll look at
several approaches. First: the Nash model. Our goal here is to
calculate what an independent arbitrator who wanted to be "fair" (i.e.
not make interpersonal utility comparisons) to both parties would do.
This procedural fairness is sometimes substantially unfair, since
(e.g.) poor people don't get any extra weight. The solution is to
maximize the product of the utility shares, which means whoever's
marginal utility shrinks first wins (if they're the same it's split
50-50). There's also a version that drops symmetry and gives one party
a portion of the upside over their fallback position in proportion to
their "bargaining power," but this seems less illuminating.
While approach is to imagine the decision of an impartial arbitrator,
approach 2 models perfectly rational people making offers and striking
for a bit if they're rejected. Discount rates turn out to be crucial
here -- if A can borrow at 4% interest and B at 15%, A will get around
four times as much in the end. (The actual formula is A's_fallback +
(1 - A's_fallback - B's_fallback) * ((1 - B's_discount_rate)/(1 -
A's_discount_rate * B's_discount_rate)), FWIW.) The bargaining power
in the modified Nash model thus turns out to be the ratio of time
preference, making the two models equivalent.
These are both pretty unrealistic, so let's try something else. There
are now _groups_ of As and Bs pairing up and playing the division
game. (Remember the division game? There's two people and a pot of
money. Both people name a percentage. If the percentages add up to
100% or less, they each get that percent of the pot, otherwise they
get nothing.) People remember what divisions were offered before, so
they try that, but occasionally try to get a little bit more. What
happens is the group settles on norms, but (on rare occasions when
everyone on one side tries for more at the same time) things tip over
into new norms. But what norm do they end up with most? In practice,
ti again turns out to be the Nash model. (Surprise!) It seems obvious
As and Bs should coordinate amongst themselves; we'll deal with that
in chapter 12.
Here's a story: a B wants to award a job worth v. But he can't decide
which A to give it to. So he offers it to the person who has the most
schooling. Schooling has no connection to the job but it shows
diligence which is hard to measure. How much money to rational As
spend on school? The answer appears to be enough that the winner nets
v/2. (The loser nets negative v/2.)
In short, as Norwegian economist Leif Johansen puts it "Bargaining has
an inherent tendency to eliminate the potential gain which is the
object of bargaining." [AS: Hmm, Elster wrote about this when he was
in Norway.] This does seem to be real: studies find that legal fees
often exceed the amounts awarded to the winner. Finally, experiments
with undergrads find cooperation is more likely when the benefits from
cooperating are bigger. [OK, I had trouble following this section.]
There are, of course, other factors in bargaining, like norms of
fairness and fear of long-term consequences. "Early business oppo-
sition to Keynesian economics in the United States apparently did not
stem so much from a failure to recognize the benefits that businesses
could reap from a reduction in macroeconomic cyclical volatility, as
from concern that a more interventionist state might also undertake
other policies of a less business-friendly nature." (202)
And thus ends part 1. Next week: capitalism.
Nathan Torkington
> I assume everyone else has given up on the book by now, so I figured
> I'd just summarize this chapter for you
Long since been left whimpering in the dust, yes, but please do keep
up your summaries. I'm getting a lot from them.
Thanks,
Nat
Chris Mealy
a few days.
Benj. Mako Hill
>
> I'm still slogging through the math in chapter 4. I'll be caught up in a
> few days.
I'm still somewhere in Chapter 3 but will hopefully be catching up this weekend.
Later,
Mako
--
Benjamin Mako Hill
ma...@atdot.cc
http://mako.cc/
Creativity can be a social contribution, but only in so far
as society is free to use the results. --GNU Manifesto
Jacob Rus
>> few days.
>
> I'm still somewhere in Chapter 3 but will hopefully be catching up this weekend.
Similarly, I'm just through chapter 1... didn't get a copy of the book
until a few days ago, but I'll try to catch up in the next week or so.
Cheers,
Jacob