me:
>>BTW, if this story is revealing, that indicates (once again) that
game theory can say something about the
world, as long as we don't obsess with equilibrium situations (Nash or
otherwise).<<
Gil Skillman wrote: > I would have rather said "game theory can say
something about the world, so long as we are careful about specifying
the context within which equilibrium might arise." ... Equilibrium is,
of itself, not all that restrictive an idea (equilibria can evolve
continually, for example); it just provides a focal point for
analysis.<
Note my use of the word "obsess" above. There was a reason I used that
word; I did not choose it randomly. The problem with received economic
theory does not arise form the concept of equilibrium _per se_.
Instead, the problem arises from the concept's reification (its
treatment as being real somehow) and its becoming the sole center of
all theoretical attention. This practice fits well with their over-use
of mathematics as an idealized representation of the world. (Note that
it's not just the neoclassicals who fall for this trap; Neo-Ricardians
do, too.)
It should be stressed that the attainment of equilibrium is a _special
case_, not the general rule. But just because it's a special case does
not mean that it's totally irrelevant.
For example, consider the tendency toward the achievement of
equilibrium that was central to Ricardo & Marx: the idea that the
rates of profit in different sectors tend toward equality. If, for
example, we want to understand the relationship between prices and
values (often misnamed the "transformation problem"), we need to have
some notion of how this relationship would look if the tendency toward
equalization of profit rates were totally realized. (We should always
talk about equilibrium using the subjunctive voice, though it's hard
to stick to this rule. Grammar is already too hard.)
Because of its lack in this department, a lot of the ideas presented
by Drewk _et al_ are inadequate, lacking general applicability. That
is, the fact that (some of?) Drewk's models don't work in an
equilibrium situation is a severe weakness for them. Drewk and his
colleagues seem to have produced some nonsense by rejecting the notion
of equilibrium completely. They seem to have produced a mirror-image
of the neo-Ricardian theory, in which equilibrium always applies.
(However, note that I am not an expert on this debate. Drewk's school
may be able to convince me that I'm wrong.)
Though the concept of equilibrium can be useful at times, people
interested in understanding the real world -- rather than dwelling on
the logical limitations of Drewk's school of thought and the purely
logical level of analysis -- need to be conscious of the
counter-tendencies that also exist in the world as we know it.
Capitalist markets involve irregular endogenously-generated
technological change, efforts to attain monopoly, and rent-seeking,
which irregularly disrupts any equilibria attained or counteracts
movements toward equilibrium. The real world that we see in front of
us is _not_ a system that moves toward equilibrium. Instead, it a
product of the combination (the resultant?) of both movements toward
equilibrium and endogenous shocks that move markets away from
equilibrium.
(Somewhat similarly, the orbit of the Moon is the result of the
combination of its movement toward equilibrium (crashing into the
Earth) and its inertia (moving in a roughly straight line away from
the Earth, a path inherited from history.)
The concept of equilibrium makes the most sense in an isolated
competitive & static market, where supply and demand tend to equalize
when the market is left alone (or if monopoly prevails, where the firm
determines its profit-maximizing price and quantity). But it would be
a mistake to generalize from that situation to all markets. For
example, oligopolistic rivalry produces dynamic results, continually
changing markets, with new product differentiation, new advertising
campaigns, etc.
Further, the idea of equilibrium covers a multiple of concepts. It
includes not only the silly neoclassical notion of steady-state growth
with an aggregate production function (and with saving determining
investment!) but also the knife-edge equilibrium seen in Marx's
reproduction schemes and Harrod's model of growth. In the latter case,
for clarity's sake, we should re-name "equilibrium conditions" as
"conditions needed for harmonious growth." Or we might nod to
Leijonjufvud and Clower, and so refer to _notional_ equilibrium.
We should also note the various real-world forces disrupting this
harmony when or before it is achieved (i.e., endogenous forces
driving the economy into crisis) and those that encourage recovery
from crisis (e.g., rising unemployment, which depresses wages and
spurs profits to rise). We should also note the fact that the economy
may have more than one equilibrium at any one time. (For example, the
late Joan Robinson pointed to different kinds of growth paths, golden,
leaden, tin, uranium, etc.)
People who study psychology and physics for a living do not use the
concept of equilibrium much if at all. On the other hand, chemists use
the concept a lot. That suggests that we should be very careful. We
should not presume that equilibrium concepts should be applied in all
contexts. That is, it would be wrong to make the _a priori_ assumption
that all of the world analyzed by economists fits the chemist's
world-view and not the psychologist's or physicist's.
All this says that even though the equilibrium concept "provides a
focal point for analysis," it would be a mistake to focus too much on
it. To obsess on equilibrium situations would be to imitate the drunk
who searches for his car keys where the light is good rather than near
where he actually lost his keys. Our focus should not be on abstract
concepts but on trying to understand the world.
In the middle of the quote above (where the ellipsis is), Gil writes:
> Without some notion of equilibrium, anything feasible can happen in
any given setting, and if that's all you can say, then game theory --
or any other positive social theory, for that matter -- doesn't have
anything useful to say about the world. <
The fact is that in a prisoner's dilemma game, when actually enacted
in a lab, does produce a lot of results that don't fit with
equilibrium theories. The equilibrium theories do say something. But
our focus should be on the actual results, rather than on forcing the
world into the equilibrium rubric. The equilibrium theory is something
that should be tested empirically rather than being treated as _a
priori_ true. (Calling Dr. Popper! STAT!)
Even without the concept of equilibrium, I think game theory does have
something useful to say about the world. It can represent some of the
situations -- dilemmas -- that people find themselves in, the various
options they have, and the results of their decisions. Sure, it makes
game theory be a lot like the many 2 x 2 boxes that you often see in
sociology books, but if our focus is on the real world of sentient
creatures living in society, that may be as good as it gets. People
are ornery, as Freud once said (not!). We may not be able to fit the
world into the equilibrium strait-jacket. It's good to know if that's
so or not rather than making the presumption that it fits there.
I like a theory with a clear prediction, but it's important to realize
that the world outside our skulls does not correspond exactly to the
imaginary world within it.
What about other positive social theory? an old hairy German guy once
developed one of these. He posited the idea that the forces of
production (technology, the human ability to produce use-values, etc.)
develops over time, changing in both quantitative and qualitative
ways. (It's not just that we can produce more, but that the products
and processes used to produce them differ over time.) On the other
hand, the institutions that people create to try to organize the
economy and society (the relations of production) also develop over
time, changing in small and large ways.
To a large extent, the development of the forces of production depends
on the relations of production (as, for example, capitalists seek out
only those technologies that promote profitability). Simultaneously,
the relations of production reflect the forces of production (as, for
example, the application of a new method of combining material inputs
requires new ways of getting workers to work together).
The idea of equilibrium can show up here: there is notional harmony
that might (in theory) occur, where the forces and relations of
production mesh _perfectly_, so that the social system attains
equilibrium, perhaps even a dynamic equilibrium. (Paul Baran developed
this kind of theory, in his POLITICAL ECONOMY OF GROWTH.)
But I think that Marx was right to eschew the orthodox economist's
obsession with equilibrium to instead emphasize the normality of the
_uneven development_ of the forces and relations. He was right to
emphasize what Mrs. Robinson (here's to you!) called "historical time"
rather than being stuck with the idealized "logical time" of current
economic theory. (I don't think he even chose between these two,
however, since he started as a dynamic thinker, following Hegel,
rather than with static and abstract world-view. Lucky guy.)
The forces and relations can get out of sync with each other,
encouraging crises, class struggle, and changes in institutions. This
complicated result implies that we could move toward other, distinctly
different, combinations of forces and relations. More than one
equilibrium (as it were) might be achieved from this mess. This
indicates a role for active human agency in determining the actual
results, where people are not simply results of economic forces but
creators of different conditions.
I think that this theory says a lot about the world without being
stuck on the Procrustean bed created by obsession with equilibrium
thinking. If we lower the level of abstraction a few notches, stirring
in a bit of over-determination, it can even help us understand current
social and political events. We may not be able make very concrete
_predictions_ about what's will go on in the future, but that's
because of the nature of the future in the real world: it's uncertain.
>And while I'm at it, a couple of observations about the repeated PD
problem for what they're worth: Trigger strategies, or more generally
"optimal penal codes," if credible, turn the supergame corresponding
to the indefinitely repeated PD game into a coordination game. So do
norms of reciprocating behavior.<
As I noted from the start, I wasn't talking about repeated games. But
I was talking about the state using its power -- backed by norms of
accepting property rights and the like -- converting a "game" into a
non-PD situation.
> Laws and states don't solve prisoners' dilemma problems of themselves--after
> all, laws can be broken and state actors often don't do what they're
> "supposed" to do--they just change the context within which prisoners'
> dilemmas are played... <
Right. That's one reason why we need a dynamic social theory rather
than obsessing on PD and other such games. As usual, the empirical
deserves more attention than the purely theoretical.
> A characteristic feature of coordination games is that they have multiple,
> Pareto-rankable equilibria.<
Can't they also have equally-ranked equilibria, as with the so-called
"war between the sexes" game? BTW, I notice that game theorists often
point to the existence of multiple equilibria and throw up their
hands. They seem upset by the fact that equilibrium isn't unique and
then look for ways to make it unique (trembles and all that: see the
Hargreaves Heap & Varoufakis book on game theory). Why? In the case of
the "war between the sexes," why can't the Ma and Pa get together and
_talk_ in order to decide which equilibrium result to choose? Maybe
they could choose to alternate between the two equilibria. That is, Ma
and Pa might change the rules of the game.
> You could get the cooperative outcome, or you could get cruddier outcomes,
> all the way down to perpetual mutual "defection" or the "war of all against
> all" [posited by Hobbes]. Thus it might be that the ultimate social
> problem, once you get past the Hobbesian state of nature, is most
> appropriately represented by a coordination game.<
I don't get this. You seem to be saying that the ultimate social
problem is the Hobbesian state of nature (which might be seen as an
extension of the PD game). But then the issue is not the basic need
for cooperation (avoiding mutual defection) but instead coordination
(the choice among different non-defection equilibria). Or maybe you're
using these two C words differently than I.
--
Jim Devine / "The radios blare muzak and newzak, diseases are cured
every day / the worst disease is to
be unwanted, to be used up, and cast away." -- Peter Case ("Poor Old Tom").
