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Austrian Economics
and Game Theory:
a
Stocktaking and an Evaluation
Nicolai
Foss
RESPECT
Department
of Industrial Economics and Strategy
Copenhagen
Business School
Nansensgade
19,6
1366
Copenhagen K
Denmark
June
16, 1999
1
Austrian
Economics and Game Theory:
a
Stocktaking and an Evaluation
Abstract
I
discuss the merits and drawbacks of game theory in economics from
the
perspective of Austrian economics. I begin by arguing that
Austrians
have neglected game theory at their peril, and then suggest
that
game theoretic reasoning could be one way of modelling key
Austrian
insights. However, admittedly some aspects of game theory
don’t
square easily with Austrian economics. Moreover, a major
stumbling
block for an Austrian acceptance of game theory may lie in
the
traditional Austrian resistance to formal methods.
Acknowledgments
The
comments of Pierre Garrouste, Ulrich Witt and two anonymous
reviewers
of this journal are acknowledged and appreciated.
JEL-Classification
B21,
C70, D5
2
I. Introduction
This
paper is founded on the conviction that in order for the Austrian critique of
mainstream
economics to have true bite and relevance, Austrians should be aware
of
and relate to the latest advances in mainstream economics. This may sound as a
truism,
but it is nevertheless the case that the Austrians have been particularly bad
at
relating to one very important trend in the development of mainstream
economics
during the last two decades: the rise of game theory. This is a serious
problem
for several reasons, most notably for the simple reason that game theory
is
so crucially important in contemporary mainstream economics.
As
Franklin Fisher (1990: 113) noted, in the nineteen-eighties, “... game
theory
came to the ascendant as the premier fashionable tool of microtheorists”,
and
it has certainly not lost that position, as inspection of virtually any
mainstream
journal
will confirm. Thus, the arguably major mainstream theoretical advances in
the
1980s and 1990s, such as the theory of contracts and the theory of auctions,
have
been almost completely driven by game theory methods.1 Though
admittedly
simplistic, there is much to say in favor of the view - put forward with
much
force by Rizvi (1994) - that general equilibrium theory died and game
theory
to a very large extent took over as the analytical core of modern mainstream
economics.
However, Austrians continue to direct their criticisms at general
equilibrium
theory (e.g., Kirzner 1997; Boettke 1996), but neglect game theory.
They
do so at their peril.
The
amazing growth of influence of game theory in economics is in itself an
important
reason why Austrians should take a stand on game theory. A further
reason
is that game theory has been argued to address exactly the dynamics of the
market
process that Austrians have so vigorously criticized mainstream economics
for
neglecting.2
Indeed,
the argument may be put forward that the Austrian
dynamic
conception of the market process as one of entrepreneurial discovery has
been
made redundant by advances in applied game theory, particularly in the
context
of industrial organization. Although such is hardly the case, it does
suggest
that, from an Austrian point of view, the new game theoretical industrial
organization
(IO) (e.g., Krouse 1990) may be seen as an advance relative to the
oldfashioned
structure-conduct-performance
IO which has for a long time and for
good
reasons been strongly criticized by many Austrians (e.g., Armentano 1982).
In
turn, this suggests that from an Austrian point of view, there may be both cons
and
pros to game theory (and to its applications in economics).3 I shall be taken
up
with
analyzing these in the present paper.
Because
there are both pros and cons to game theory, Austrians need to
consider
these and make up their mind. My own conclusion is that the pros
outweigh
the cons and that Austrians are well-advised to take an interest in game
theory
and even feature game-theoretical methods in their works. Granted, there
is
much that is objectionable in game theory from an Austrian point of view. Thus,
Austrian
subjectivism may be argued to rule out, for example, the common
knowledge
assumption,4
the
idea of consistently aligned beliefs,5 and the seeming
quantifiability
of individual utilities, as reflected in supposedly objective pay-offs.6
3
Indeed,
sometimes game theorists indulge in excesses that not even proponents of
the
more extreme versions of general equilibrium theory would engage in, such as
the
basic idea in much of game theory that agents, even in very complex settings,
can
coordinate their strategies on any desired equilibrium.7 Moreover, the players
that
populate game theory models come equipped with even more knowledge and
rationality
than has been standard fare in mainstream economics. Finally, the
notion
of the market as one of rivalrous entrepreneurial discovery in the
Kirznerian
sense (Kirzner 1973, 1997) is not present in game theory (in spite of the
effort
of Littlechild 1979).
On
the other hand, it is also fair to say that the frontiers of contemporary
game
theory are to a considerable extent taken up with issues that have been
central
in Austrian economics for a very long time. Among such issues are how to
model
players’ subjective perceptions of other players and of the game (e.g.,
Littlechild
1979; Rubinstein 1991); learning processes (Crawford and Haller 1990);
and
the role of “rules of conduct” (Hayek 1973) and various (other) institutions in
stabilizing
beliefs and expectations. This may not constitute sufficient grounds for
some
Austrians to embrace game theory. However, it may be argued that game
theory
and its application to economics ought to be judged against what came
before
it, namely general equilibrium theory. And from such a perspective, game
theory
may be seen as a distinct advance - also to Austrians. Indeed, something
like
this was clearly articulated by Austrian fellow traveller, James Buchanan
(1997:
71) when he recently observed that
[a]
major change in economic theory may have occurred in mid-century
when
the theory of games provided an alternative mathematics to the
marginalist
calculus - a mathematics
that carries important implications
for
the very way that economists conceive what their enterprise is all
about
(Von Neumann and Morgenstern 1944). In the theory of games,
attention
is immediately focused on the interaction process as such ...
During
the second third of the century, the ongoing dominance of the
maximization
paradigm tended to obscure the potential contribution
that
game theory’s elegance can make towards restoring ... the
catallactic
focus of economic theory.
The
design of the paper is the following: I begin by providing some brief
background
material to the discussion, notably on the history of game theory,
before
I turn to a more sustained critique of the Austrian neglect of game theory. I
then
discuss the pros and the cons of game theory from an Austrian point of view,
before
I finally place the discussion in the context of the broader Austrian critique
of
formal methods.
II. Game Theory: Some Background
To
a large extent, game theory is an import from mathematics.8 The two key
persons
in the early development of the theory, John von Neumann and John
Nash,
were both trained mathematicians, and many of the crucial papers have
4
been
(and continue to be) published in mathematics (and theoretical statistics)
journals.
However, an Austrian economist was also instrumental in the early
development
of game theory. As recent research has documented, there was a
source
of disagreement and confusion in the very different backgrounds and
contextual
features of the authors of Theory of Games and Economic Behavior (1944).
Von
Neumann’s background was in the foundations of mathematics and his
involvement
in economics had related to existence proofs of competitive
equilibrium
and growth theory, as well as a general wish to help reforming social
science
(not just economics) through the supposedly more “scientific” use of
thoroughgoing
formalization. Though substantively important, his contributions
to
economics were few.
Von
Neumann’s co-author, Oskar Morgenstern, was an Austrian economist,
of
the same generation as Hayek and Machlup, but (together with Leo Schönfeld-
Illy
and Paul Rosenstein-Rodan) belonging more to the circle of Hans Meyer than
to
the Mises Kreis. Morgenstern had taken over from Hayek as the director
the
Vienna
Institute for Business Cycle Research, a position he kept until the Anschluss
in
1938, where he - while
staying at Princeton University - lost that position.
However,
in Princeton Morgenstern met Von Neumann and quickly embarked
upon
the project that became The Theory of Games and Economic Behavior.
Morgenstern’s
primary role in the project appears to have been that of the
asker
of provocative questions and supplier of ideas on plans, plan compatibility
and
the role of time in economic affairs - subjects that he had treated in a number
of
earlier publications (Morgenstern 1928, 1935a&b). These earlier works were
clearly
inspired by Hans Meyer (e.g., Meyer 1932) in their concern with individual
plans,
but also were clearly related to Hayek’s (1937) interest in the interaction and
compatibility
of plans. It is not difficult to see the link between mixed strategies
in
two-person, zero-sum games, and the famous Holmes-Moriarty parable from
Morgenstern
(1935a: 173-4):
Sherlock
Holmes, pursued by his opponent, Moriarty, leaves London
for
Dover. The train stops at a station on the way, and he alights there
rather
than traveling on to Dover. He has seen Moriarty at the railway
station,
recognizes that he is very clever and expects that Moriarty will
take
a faster special train in order to catch him in Dover. Holmes’
anticipation
turns out to be correct. But what if Moriarty had been still
more
clever and had foreseen his actions accordingly? Then, obviously,
he
would have traveled to the intermediate station. Holmes, again,
would
have had to calculate that and he himself would have decided to
go
on to Dover. Whereupon, Moriarty would again have “reacted”
differently.
Because of so much thinking they might not have been able
to
act at all or the intellectually weaker of the two would have
surrendered
in the Victoria Station, since the whole flight would have
become
unnecessary.9
Moreover,
Morgenstern’s story anticipates quite modern discussions of the
paradoxes
of common knowledge (see Bicchieri 1992) and, more generally, the role
of
agents’ beliefs in game theory. The Morgenstern parable would seem to
5
indicate
the impossibility of perfect foresight equilibria, or at least of perfect
foresight
processes leading to such equilibria in situations of conflict (O’Driscoll
and
Rizzo 1985). It therefore indicated, as Morgenstern (1935a) pointed out, the
necessity
of inquiring into the disequilibrium market process, characterized by the
less
than perfect foresight of agents, of different beliefs, etc. However, in
actuality,
little of this survived in Von Neumann and Morgenstern (1944), where,
quite
in contrast to Morgenstern’s emphasis on the role of different beliefs and
imperfect
foresight in the market process, most of the reasoning took place with
reference
to static situations characterized by homogenous beliefs and perfect
foresight
(Mirowski 1992).
Historically,
game theory was initially greeted with considerable enthusiasm
in
the economics profession (Rizvi 1994; Hargreaves Heap and Varoufakis 1995;
Leonard
1995) - an enthusiasm
that, however, quickly faded away as application
turned
out to be harder to accomplish than initially envisaged. Much of the reason
was
that most game theory discussions and applications were limited to the zerosum,
two-person
games that Von Neumann and Morgenstern had been primarily
taken
up with. But another reason, which is perhaps more interesting in the
present
context, is that Von Neumann and Morgenstern’s book was actually
interpreted
as a major attack on the emerging Hicks-Samuelson orthodoxy
(Leonard
1995: 731).10
Since
this orthodoxy was interpreted as an attempt to
basically
found the core areas of economic analysis on the competitive equilibrium
model,
the game theory concern with small-scale interaction was interpreted as a
provocative
new agenda, and to some extent suppressed as a dangerous heresy
that
introduced unnecessary complications.
Given
this, it is ironic that one the first applications of game theory in
economics
to make a serious impact is Debreu and Scarf (1963). Not only was this
paper
published 19 years after the publication of von Neumann and Morgenstern
(1944),
but it also utilizes game theory in the context of what should be seen as an
attempt
to further the general equilibrium program.11 Somewhat earlier, Arrow
and
Debreu (1954) had made reference to Nash (1950),12 but only because they
were
inspired by Nash’s use of the Kakutani fixed point theorem to prove
existence
of equilibrium in n-person games. Of course, Martin Shubik had
published
his pioneering application of game theory to IO, Strategy and Market
Structure: Competition, Oligopoly, and the Theory of Games in 1959. But it
seems to be
a
fair judgment13
that
the first contribution to make a truly substantial impact is
the
Debreu and Scarf paper. However, after the Debreu and Scarf paper, there is
again
a long time lag, this time between the application of game theory and its
widespread
acceptance, the take-off period being the beginning of the 1980s,14 and
the
virtual dominance of economics being completed around the end of that
decade.
Speculating
about the timing of this, Rizvi (1994) argues that the primary
factor
explaining the spread of popularity of game theory was that it had become
apparent
for most theoretical economists that the general equilibrium project had
encountered
severe difficulties. Among these difficulties was the much discussed
result
due to Mantel, Debreu and Sonnenschein result about the arbitrariness of
6
excess
demand functions in GE theory and the difficulty of handling imperfect
competition
in GE. In this situation, game theory simply came to the rescue of
theorists
and saved them from the inherent arbitrariness of GE theory.
There
is arguably much truth to this story, although it also underestimates
the
fact that (partial equilibrium) industrial organization economics became a very
fashionable
field in the 1980s, and that field leaned heavily on game theory. In
other
words, game theory in economics did not just emerge because of certain
logical
problems in general equilibrium; it also took hold because it was inherently
better
equipped than general equilibrium theory to deal with a number of issues.
This
was anticipated in the early 1970s by Oskar Morgenstern (1972) when he
observed
that economists had, sooner or later, to abandon “the Walras-Pareto
fixation”,
that is, the preoccupation with competitive equilibrium, and turn to
analysis
that includes much more comprehensively the formation of beliefs, rivalry
and
competitive struggle - issues that Morgenstern implied were much more
adequately
treated in the game theory that he had helped found.15 It is
appropriate
at this point to turn to the Austrian critique of mainstream theorizing,
for
if there are any economists who have urged the profession to abandon “the
Walras-Pareto
fixation”, it is certainly the Austrians.
III. The Austrian Critique of the Mainstream
At
least since the socialist calculation debate - and possibly earlier16 - the perhaps
main
target for the scholarly critiques of Austrian economists has been the general
equilibrium
model. Although some modern Austrians - such as Mises (1949) who
constructed
his own general equilibrium pendant, “the evenly rotating economy” -
have
seen some merit in the use of the construct as an analytical foil, other
Austrians,
such as Lachmann (1986), have rejected general equilibrium theory
altogether
and for all purposes. Presumably, all Austrians strongly reject the
Chicago
“equilibrium always” strategy in which virtually all observed economic
phenomena
are interpreted as realizations of an underlying stochastic general
equilibrium
model.17
In
fact, Austrians continue to debate the merits and
(particularly)
drawbacks of the general equilibrium model (Kirzner 1997; Boettke
1997).
Indeed, Austrians still tend to identify (the core of) mainstream or
neoclassical
economics with the general equilibrium model. To quote Israel
Kirzner
from his recent Journal of Economic Literature survey of recent Austrian
work,
it is at “the basis” of the Austrian approach
...
that standard neoclassical microeconomics, for which the Walrasian
general
model (in its modern Arrow-Debreu incarnation) is the
analytical
core, fails to offer a satisfying theoretical framework for
understanding
what happens in market economies (1997: 61).
One
may, of course, seriously question whether any of the major contributors to
GE
theory (apart, possibly, from Fischer Black and Robert Lucas) have really ever
thought
that GE theory offers “a satisfying theoretical framework for
7
understanding
what happens in market economies” (see Hahn 1984), but that is
not
the critical point here.
Rather,
the point is that for a number of reasons, the centrality of the general
equilibrium
model in the critiques of Austrians and their apparent identification of
it
with (the core of) mainstream economics may be increasingly misguided. First,
general
equilibrium doesn’t at all hold the same sway over the profession as it
possibly
did two or three decades ago.18 Second, to some extent, it is descriptively
true
to say that general equilibrium theory is dead - or at least dying. Third,
as
we
have seen already, the dominant paradigm today is game theory and not the
competitive
equilibrium model. Rather, the latter is increasingly seen as a special
case
of the former. Hicks and Samuelson have given way to Morgenstern and Von
Neumann
(or to Nash, Aumann, Rubinstein, Selten, and Harsanyi).
The
problem is that Austrians seem to be unaware of this development, or at
least,
they have not explicitly reacted to it. However, the position here is that
Austrians
should take a stand on game theory.19 It is fully acceptable for a small
group
of economists with a distinct outlook to carve out a niche for themselves,
and
Austrians may be most comfortable swimming in the waters of methodology,
economic
policy and comparative systems. On the other hand, it is hard to deny
that
perhaps the most remarkable achievement of the Austrian school in the last
decades
- the refinement
of the Austrian view of the market process in the works
of
Israel Kirzner - relates
directly to issues that are central to game theory. Thus,
non-Austrians
may ask how the Austrian view of the market process relate to, say,
game
theoretic IO, and they may be entitled to expect an Austrian answer.
Indeed,
when Kirzner (1997: 64) notes that modern presentations of the
entrepreneurial
discovery approach have tried to
...
demote the concept of perfect competition from its position of
dominance
in modern neoclassical theory, in order to replace it by
notions
of dynamic competition (in which market participants are,
instead
of exclusively price takers, competitive price - and quality -
makers),
any modern game theoretic IO economist is likely to
retort that this is exactly what
been
has going on in IO in the last two decades.
A
further related consideration brings us back to the point that the Austrian
critique
of equilibrium may be slightly out of date. When Austrians are criticizing
“equilibrium
economics”, they are criticizing, as we have seen, the competitive GE
model.
Indeed, “equilibrium” in Austrian texts is almost always synonymous
with
optimal competitive general equilibrium, a view that is implicitly defended
by
pointing to the importance of the latter model (e.g., Kirzner 1997).20 But surely
there
is much more to equilibrium than this model. The basic textbook monopoly
model
does not, for example, portray the price-taking behavior criticized by
Austrians.21 And what about
ordinary Marshallian partial equilibrium; do the
reservations
that may be hold with respect to GE also apply here? More to the
point,
application of game theory to economics has now resulted in a plethora of
equilibrium
concepts, most of which are refinements of the basic Nash equilibrium
8
concept,
such as mixed-strategy Nash equilibrium (in two- or many-person
games),
perfect equilibrium, trembling hand equilibrium, etc. Are these
equilibrium
concepts equally problematic as competitive equilibrium? All of
them?
Only some of them? Why? In order to ease the process of relating to game
theory,
I shall in the following present two different Austrian views of game
theory,
one against and one for.
IV. Against Game Theory: a Negative Austrian View
Among
the few Austrians who have explicitly commented upon game theory is
Ludwig
von Mises (1949). Characteristically frank, he entertained a hostile view
of
game theory:
There
is not the slightest analogy between playing games and the
conduct
of business within a market society. The card player wins
money
by outsmarting his antagonist. The businessman makes money
by
supplying customers with goods they want to acquire … He who
interprets
the conduct of business as trickery is on the wrong path
(p.116).
Writing
in 1949, Mises appears justified in his critique of the zero-sum character of
the
game theory of his day. And one can certainly direct his objection against
modern
game theoretical IO that fanatically attempts to reduce virtually all market
phenomena
to a matter of “oursmarting” opponents. However, game theory has
come
a long way since 1949. And there are many other Austrian-style critiques
that
may be launched against game theory. These are discussed in the following.
Formalization. One fundamental reason why Austrians should
dislike game
theory
is that game theory uses formal methods, a reason that may be further
supported
by the Misesian position (Mises 1949) that there are no constants in
human
and that therefore quantitative and formal methods are not warranted in
the
social sciences.22 I confess to finding this view both superficial and dangerous,
first,
because it seems to rest on a conflation of “formal” and “quantitative”, and,
second,
because it amounts to a wholesale rejection of all formalization in
economics.
While formalization may often go too far and live a life of its own,
although
its advocates may have grossly oversold it in many instances, and
although
it seldom brings much that is genuinely new,23 formal modelling is often
simply
the only way to handle a complex world. It is exactly because it is so
difficult
to analytically keep track of “the everyday business of living” (to use
Marshall’s
terms) that formal modelling may (sometimes) be useful - not, as
Boettke
(1996) thinks, the reason why it is of little or no value. (More about this
later).
Misrepresenting Human Action. A more
substantial objection is that game
theory
appears to either equip agents with hyper-rationality (standard game
theory)
or portray them as completely stupid programmed puppets (evolutionary
9
game
theory) - both arguably
denials of the praxeological character of human
action
(Mises 1949). Thus, in many (standard) game theory analyses, agents are
supposed
to know things (e.g., all other players’ preference orderings) that they
wouldn’t
even know in the canonical GE model. In these respects, game theory is
sometimes
epistemically more extreme than GE theory. In evolutionary game
theory,
on the other hand, one goes to the other extreme and portrays agents as
following
rigid rules, even if these turn out to be completely irrational.24 The
critical
point here is that both approaches - the standard and the evolutionary
game
theory approaches - essentially
imply that the entrepreneurial process of
discovery
becomes suppressed: in the standard approach there is no need for it,
because,
roughly, agents already know all that is worth discovering, and in the
evolutionary
approach, they are too stupid to discover anything anyway.
Equilibrium Methodology. Closely related to this,
the coordination
problem
that Hayek (1937) forcefully highlighted in the economics of his day is
still
very much present in most of game theory; most game theorists simply
assume, without giving substantive reasons for this, that
agents can coordinate their
strategies
on any desired equilibrium through purely ratiocinative processes, and
without
any genuine learning, discovery, surprises, etc.. Game theory rests on
equilibrium
notions, and game theorists, like earlier neoclassical theorists, have
spent
comparatively little time examining the process of adjustment to an
equilibrium.
As
has already been suggested, much recent work in game theory has
consisted
in refining various equilibrium concepts (Fudenberg and Tirole 1995). In
contrast,
the basic issue of how players actually home in on a coordinated state -
how
the Hayekian knowledge problem is actually solved - has been offered less
attention.
Indeed, the suspicion may be entertained that game theory has become
so
popular because it seems to solve the coordination problem (or, stability of
equilibrium
problem) that characterized general equilibrium theory. It does so,
however,
by appeal to pure ratiocination: agents simply reason their way to
equilibrium,
as it were -
a
procedure expounded already by Von Neumann and
Morgenstern
(1944: 146-148).
Some
justification for focusing on only Nash equilibria (or, per implication,
derived
equilibrium concepts) was provided by Aumann (1974). He argued that if
pre-play
communication was allowed, but players couldn’t commit to certain
actions,
they would only consider self-enforcing outcomes, that is, Nash equilibria,
the
basic reason being that no external enforcement was available. However, the
basic
justification for focusing on outcomes that are Nash still mostly proceeds in
terms
of pure ratiocination; there is an underlying assumption that players can
coordinate
their strategy choices on any desired equilibrium.25 But if that is the
case,
the hand running the market is very visible indeed; standard game theory
analysis
has difficulties make sense of the notion of unintended consequences,
simply
because it makes so strong assumptions about the epistemic powers of
individuals.26
It
is worth confronting this with Morgenstern (1935a&b) and Hayek’s (1937)
analysis
of the connection between knowledge and equilibrium. In terms of game
10
theory,
they both questioned the legitimacy of beginning from what is essentially
an
existence claim, namely that if rational players have commonly known and
identical
beliefs about all other players’ strategies, then those beliefs are
consistent
with
some equilibrium in the game. The problem is that nothing is said about the
origin
and formation of beliefs. This is bad enough in itself. However, there is
also
the problem it is in principle possible that although there exists an
equilibrium
in players’ strategies, they may never be able to realize that
equilibrium.
Clearly, simply proceeding by eliminating various equilibria by
means
of various refinement procedures will not do. There is still a need to
rationalize
the emergence of beliefs that can sustain the final equilibrium - and
here
existing game theoretical work is sparse compared to the enormous amount
of
work that is exclusively concerned with game theoretic equilibria.
V. For Game Theory: an Austrian View
The
purpose of this section is to present arguments in favor of game theory that
should
appeal to Austrians. Also, many of the arguments in favor of game theory
in
this section answer the critiques of game theory listed in the previous
section.
Game Theory as a Part of the Austrian Tradition. A favorable
Austrian
view
of game theory may begin by noting that game theory is simply one
outgrowth
of the Austrian research program founded by, in particular, Menger
and
Böhm-Bawerk.27
Specifically,
game theory, and its applications in economics
(particularly
in IO), is arguably Austrian in its concern with plan formation and
plan
consistency, in its much more explicit treatment of the role of time in
economic
affairs, and in its insistence that the competitive equilibrium model is
merely
one (very unrealistic) model among many others and certainly not the one
that
all of economics should be founded upon.28
In
such a reading, there is rather direct line of influence from Menger and
Böhm-Bawerk’s
concern with less than perfectly competitive situations (e.g.,
Böhm’s
famous horse-trading example, Schotter 1974) over Hans Mayer’s (1932)
concern
with plan-formation and -interaction to Morgenstern (1935a&b) and
Hayek’s
(1937) concern with the epistemic preconditions of equilibrium to
Lachmann’s
(1986) radicalization of the very same themes. And Von Neumann
and
Morgenstern (1944) is simply one, formal, instantiation of this Austrian
tradition,
although any Austrian would regard as merely a very first step than
needed
to be taken in a much more dynamic direction. Andrew Schotter (1992:
97)
argues in favor of this position:
In
terms of economics ... [Von Neumann and Morgenstern 1944] was a
natural
outgrowth of several earlier ideas of Morgenstern’s and must be
appreciated
as a milestone in the evolution of Austrian economics.29
Such
an interpretation is admittedly somewhat extreme. For example, it
would
need to adopt a somewhat peculiar understanding of Austrian economics;
for
example, it needs to suppress the traditional Austrian critique of
formalization.
11
Moreover,
it overlooks that the fact that rather few of Morgenstern’s distinctly
Austrian
themes actually emerged in Von Neumann and Morgenstern (1944).
However,
one could perhaps defend it by taking a broader view, and see
the“Austrian’ness”
of game theory more as a matter of stressing the subjectivism
of
plans (i.e., the “beliefs” that underlie “strategies” in games), the critique
of
competitive
equilibrium, and the sequential nature of actions in the market process
(which
may be given to an equilibrium interpretation).
The Market Process and Entrepreneurship. Although
disequilibrium
behavior
and the market process in the Austrian sense have not been much treated
in
game theory, at least some aspects of entrepreneurial behavior and the market
process
are given to game theoretic formalization. In a splendid, but neglected
paper
published almost twenty years ago, Stephen Littlechild (1979) tried to
accomplish
exactly this, arguing that cooperative game theory could be used to
model
an entrepreneurial bargaining process, and undertook some formal
modelling
of this. Austrians have unfortunately paid no attention to this work.
Other
recent insights in game theory also offer the possibility of finding a
room
for the entrepreneur. For example, in many coordination games, there may
be
multiple equilibria, some of which may be symmetric (same pay-offs for the
involved
agents). Although repeating coordination games is one way of making
sense
of conventions (Young 1996), it can also be used to make sense of the
leader/entrepreneur,
since he can be thought of as selecting a specific equilibrium.
A
somewhat related example occurs in connection with iterated prisoners’ games.
As
is known from the Folk Theorem, even very simple iterated PD games are
likely
to have multiple equilibria (depending on what is assumed about discount
rates),
and more complex games with multiple players and incomplete
information
- that is, real
life games -
certainly
do have multiple equilibria.
There
are many implications of the multiplicity of equilibrium phenomenon
that
should be of interest to Austrians. First, it supplies a powerful argument
against
the standard mainstream instrumentalist position that because the
economy
somehow will home in on “the” equilibrium, there is no need for an
inquiry
into the disequilibrium market process. If the resulting equilibrium is
crucially
dependent on the process, this argument does not hold water. Secondly,
the
introduction of multiplicity of equilibria means that there may be a room for
the
entrepreneur, broadly understood as the agent that helps pushing the system
from
one equilibrium to another. For example, applied to firms, the Folk
Theorem
tells us that there may be many different ways of motivating cooperation,
for
example, many different ways of structuring retaliation schemes. However,
the
problem of choosing one such way - that is, make players coordinate on a
specific
equilibrium -
is
fundamentally a coordination problem whose solution
may
require the intervention of somebody equipped with “entrepreneurial”
qualities,
broadly conceived (for further examples and discussion, see Foss 1998).
Later
work on learning processes in games may also be argued to have taken
a
broadly subjectivist stance. Although much game theory begins from a situation
in
which players have perfect knowledge of virtually anything but a few variables,
a
growing literature asks much more radical questions, such as, How do players
12
acquire
knowledge of the game in which they take part? How do they acquire
knowledge
of other players? If several equilibria exist in the game, how do players
over
time coordinate on one equilibrium? Etc. This literature is a considerable
advance
relative to earlier, non-game theory approaches to learning that tend to
look
on only competitive situations, represented as sequences of temporary
equilibria.
This means that severe restrictions are placed on the possible behaviors
of
agents, because they have to respect the restrictions imposed by a competitive
set-up
(Kreps 1990). In contrast, game theory allows what seems to the Austrian to
be
the natural procedure: first we specify the behaviors of agents and then
we
examine
the interaction of those behaviors. Thus, disequilibrium situations are
given
to formal treatment.
In
a fascinating study, which is representative of a number of similar studies,
Crawford
and Haller (1990) discuss the issue of how agents may learn to cooperate
in
the context of a repeated pure coordination game30 with imperfect information.
The
imperfection of information in the games that they consider is a matter of
strategic
uncertainty, stemming from the presence of symmetric equilibria and the
complete
absence of any focal points.31 The only way in which players can
communicate
is through playing the game. However, eventually sort of
convention
(or focal point) about which strategies to play will emerge and produce
optimal
subgame perfect equilibria. Thus, to put it in Austrian terms, there is no
end-state
(the subgame perfect equilibrium) existing ontologically separate from
the
process of coordination, so that indeed “order is defined in its process of
emergence”
(Buchanan 1982).
Institutions and Spontaneous Order. Game theory
ideas have been used in
a
number of attempts during the last 10-15 years to address Austrian and classical
liberal
ideas on the spontaneous emergence of beneficial institutions (e.g., Schotter
1981;
Sugden 1986, 1989; Young 1996). Indeed, game theory appears ideally suited
to
deal with issues that have traditionally been a major concern to (Hayekian)
Austrians,
such as the formation of conventions and other spontaneous orders.32 A
number
of these make the connection to Menger and Hayek explicit (e.g., Schotter
1981;
Sugden 1986). Similarly, a number of non-Austrian but clearly sympathetic
economists
(e.g., Langlois 1986; Witt 1986; Buchanan 1997; Klein 1997) have
utilized
game theory to analyze institutions, in some cases extensively.
Summing Up. To sum up, the bottomline of a positive Austrian
view on
game
theory is that, first, historically there is a close connection between
Austrian
economics
and game theory through the important influence of Oskar
Morgenstern,
second, that game theory appear to be able to address favorite
Austrian
explananda (such as spontaneously emerged rules) that standard
neoclassical
economics cannot handle, third, that game theory in economics means
that
the formal economist is no longer tied to the competitive general equilibrium
model,
and, finally, that game theory makes it possible to treat learning processes
(and
therefore also market processes) in a sophisticated way. It should finally be
added
that game theory is an area increasingly characterized by methodological
and
philosophical discussion of core issues of central interest to Austrians, such
as
methodological
individualism (Vromen 1997) and problems of how to justify
13
beliefs
(Bichieri 1993; Colman 1997; Colman and Bacharach 1998). It would appear
that
there are clear gains for Austrians of familiarizing themselves with game
theory,
and even make use of game theory in theorizing.
VI. Discussion
The
purpose of this section is to briefly discuss some further problems that
influence
Austrians view of game theory. I shall also briefly take stock on the
preceding
sections and argue that the pros are more important than the cons,
although
Austrians should not embrace game theoretically uncritically.
Different Types of Austrian Reactions to Game Theory. The way in which
Austrians
are likely to react to game theory is arguably dependent upon how they
themselves
conceive of Austrian economics. Thus, a Lachmannian or Shacklian
radical
subjectivist is likely to react with outright hostility to game theory.33 In his
view,
game theory does the bad thing that all formal theorizing does, namely it
illegitimately
portrays creative and imaginative human beings as preprogrammed,
stimulus-response
puppets. An Austrian who, inspired by Kirzner’s
work,
thinks that what fundamentally sets Austrian economics apart from other
approaches
is the emphasis on the market process as an entrepreneurial process of
discovery
of hitherto undiscovered new knowledge may criticize existing game
theory
for its neglect of this aspect. The die-hard Misesian may criticize game
theory
for its supposed introduction of “constants” in human action. Those with a
more
Mengerian “essentialist” attitude may think that formalization directs
attention
away from the important task of conceptual analysis and general inquiry
into
the true nature of social phenomena.34 Austrians with a more Hayekian
leaning
may, on the other hand, like game theory for its attempt to deal with
favorite
Hayekian themes, such as spontaneous order, the emergence of
conventions,
etc.
Austrians and Formal Modelling. There is the possibility
that ultimately the
crux
of the matter concerns Austrians’ relations to formal modeling, so that before
Austrians
can make up their mind on game theory, they need to make up their
mind
on formal methods. Formal modeling always involves mind constructs
(Machlup
1978) that are only intended to capture some aspects of reality.
Moreover,
there are things that a formal mind construct cannot do; for example,
we
cannot let the mind construct introduce actions that are completely new to us,
the
modellers. It is contradictory to model such “objective novelties” (to use
Witt’s
1989
terms). This is the limitation of all modeling. However, it is surely possible
to
model more limited versions of “novelty”, for example, to let one agent (an
entrepreneur)
introduce actions that are novel to the other agents being modeled
(as
in Littlechild (1979) or Fisher 1983).
Austrians
may object that typically formal modeling equips mind constructs
with
wildly unrealistic epistemic powers. O’Driscoll and Rizzo (1985: 21) present
an
argument against this procedure:
14
The
creator of the mind construct cannot attribute any type of
knowledge
to it that will ultimately rationalize the phenomenon in
question.
The construct ought to possess only that knowledge which, in
terms
of its position or what it deems relevant would have been
reasonable
to acquire. It is not appropriate to attribute to a farmer
construct,
for example, knowledge of demand and supply conditions in
the
steel industry or of the general equilibrium of the commodities he
grows.
While
this is indeed a strong and justified critique of at least strong versions of
rational
expectations modeling methods, and perhaps also of common knowledge
assumptions
in game theory, it is not a critique of formal modeling per se: One can
certainly
construct formal mind constructs that do conform to the requirement of
“understandability”
that O’Driscoll and Rizzo (1985: 21) impose on mind
constructs.35 The usual
mainstream argument against working with what an
Austrian
may think of as an “understandable” mind construct - that is, one whose
epistemic
powers may be much more limited than the standard rational economic
man
but who, on the other hand, is also possessed of entrepreneurial alertness - is
that
anything but perfection is arbitrary. In other words, while the perfect
rationality
(Robbinsian maximizing) model gives unequivocal answers (single-exit
solutions),
anything can happen once we leave this ideal and introduce
considerations
of bounded rationality, alertness, etc.
Well,
one obvious Austrian answer is: So what? If the real world really is
fundamentally
messy, we are likely to be fundamentally misled by models that
abstract
from this, and we are, at any rate, certainly capable of modelling messy
behaviors
and their aggregate implications, even if the modelling is much less
tractable
than much of what goes today in mainstream economics. Indeed, in
principle
many of the ideas that Austrians have focused upon - subjectivism (e.g.,
differing
expectations and knowledge), the market as a social learning process
(Hayek
1968), and entrepreneurial alertness (Kirzner 1973) - are in fact given to
formal
modelling, although formal accounts is never likely to capture the richness
of
verbal discourse. Therefore, it is to misunderstand the nature of formal
modelling
to believe that it commits one to, for example, the behavioral
assumptions
of mainstream economics, although, undeniably, these assumptions
have
historically taken hold in their specific forms precisely because they easily
lend
themselves to formalization. In sum, the fact that game theory is (largely)
formal
should not in itself constitute a problem for Austrians.
15
Good and Bad Aspects of Game Theory. It is likely
that while some
aspects
of game theory will appeal to Austrians, other aspects are likely to make
them
balk. While Austrians may appreciate the detailed modeling of agents’
information
sets and of agents’ interaction, they are still likely to criticize the
strong
equilibrium orientation in game theory, even in cooperative game theory,
as
well as the sometimes bizarre epistemic assumptions that are routinely made in
much
game theory.
However,
although there are crucial shared concepts and insights, game
theory
is not monolithic. On the most basic level, there is, for example, a
distinction
between “cooperative” and “non-cooperative” game theory. As
Aumann
(1985: 463) explains, whereas non-cooperative game theory is
characterized
by carefully detailing the “protocol” of the game, ”[c]ooperative
theory
starts out with a formalization of games … that abstracts away altogether
from
procedures … It concentrates, instead, on the possibilities for agreement”.
Hence,
the central focus on the ”core” (roughly, the contract curve in the standard
Edgeworth
box analysis) in this approach. Some Austrians may find that because
of
its emphasis on free-form, active deal-seeking, and therefore also in principle
unrestricted
discovery, a cooperative game theory view is actually more consistent
with
an Austrian view of economic activities than the more restrictive
noncooperative
approach.
However, even cooperative game theorists should be told
that
achieving core allocations is not unproblematic; that, too, requires the
entrepreneurial
process of discovery.
This
suggests that although Austrians may benefit from exposure to, and use
of,
game theory because game theory allows them to formalize some of their key
ideas,
they may also have a critical mission in game theory. For example, many
game
theorists haven’t learnt, or at least appreciated, the fundamental lesson of
Hayek
(1937) that there is a basic distinction between equilibrium for the
individual
agent and equilibrium for an economic system. The much used
assumption
of common knowledge amounts to a conflation of these two levels,
and
game theorists and those economists that use theory still need to be told. To
sum
up, then, a closer interaction between game theoretical economists and
Austrians
are likely to benefit not only Austrians, but also those who practice
game
theory.
VII. Conclusion
This
paper has been an attempt to identify the pros and cons of game theory from
an
Austrian perspective and thus perform a stocktaking and an evaluation that
hopefully
may be useful to Austrians. While there are many strong arguments
against
game theory, it is also the case that game theory may be the best existing
analytical
vehicle to choose to the extent that Austrians want to dress their
arguments
in more formal garb. Game theory allows the Austrian to come
formally
to grips with key ideas on subjectivism, coordination, rules and
institutions,
and the entrepreneurial market process. In particular, the emerging
literature
on repeated coordination games may be of appeal to Austrians because
16
this
literature asks the fundamental questions, such as how diverse players, with
different
knowledge and expectations, may eventually home in on a coordinated
state
(Crawford and Haller 1990; Young 1996).
Moreover,
it is a literature that stresses the role of beliefs rather than the role
of
(misaligned) incentives in coordination problems. This should also be
appealing
to Austrians. At least since the calculation debate, Austrians have
emphasized
that the economic problem of society is not merely one providing the
right
incentives, but more fundamentally one of coordinating knowledge and
expectations.
The emerging game theory literature on iterated coordination games
is
perhaps the first serious mainstream attempt to address some of these
coordination
problems, and it is a literature that is just too interesting for
Austrians
to be ignorant of.
The
main conclusion, therefore, is that Austrians should approach and make
use
of game theory in economics. This one important way in which Austrians can
relate
to those parts of the mainstream that are most congenial to Austrian
thought.
This is also where Austrians themselves may have something to
contribute
because of their long standing concern with non-standard coordination
problems
and with the market process. Game theorists, too, need to be told about
alertness,
entrepreneurship, learning, etc.
17
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Notes
1
Moreover,
game theory has invaded political science (e.g., Calvert 1995) and biology.
2
See
Vickers (1995) for this argument (complete with references to Hayek).
3
There
are certainly many general problems with game theory, such as the uncertainty
surrounding
the so-called “Nash project” (that all cooperative games can be reduced to non-
21
cooperative
games by modelling pre-play communication in non-cooperative terms) (see also
Tullock
1992 for some interesting reservations). In this paper, however, I concentrate
on those
aspects
of game theory that are particularly problematic to Austrians.
4
“Common
knowledge” is an approach to expectations formation that may be represented by
the
following
sentence: “Jack knows that Jill knows that Jack knows .... that X” - an infinite sentence.
For
a discussion of some of the problems of common knowledge, see Bicchieri (1993).
One problem
with
common knowledge is that small deviations from it can completely change
outcomes
(Rubinstein
1989).
5
“The
idea of consistently aligned beliefs” is closely related to a number of related
ideas, such as
the
so-called common priors assumptions. It essentially means that rational people
who have
access
to completely identical information cannot develop different thought processes
with respect
to
the issues that the information concern - an idea that doesn’t seem to
square easily with the
Austrian
emphasis on the active and creative mind (e.g., Lachmann 1986).
6
However,
this is not a serious problem, since game theorists do not assert that
utilities and payoffs
are
identical (although admittedly in simpler expositions, there is often a
conflation between
these).
Pay-offs simply reflect ordinal rankings, not cardinal.
7
For
example, this is characteristic of much of the game theoretic literature on the
theory of the
firm
(see Foss 1998).
8
In
contrast to mainstream economics (and assuming that the Mirowski story is valid
(Mirowski
1989),
game theory apparently has few, if any, obvious physics connotations. Actually,
both
Morgenstern
and Von Neumann scorned the fascination with physics that many leading
economists
have entertained. Not surprisingly, Paul Samuelson has been very critical of
game
theory
(cf. Mirowski 1992: 116n).
9
Actually,
it is conceivable that it was Morgenstern’s concern with such infinite regress
situations
that
led to the idea of a mixed (probabilistic) strategy (Holmes and Moriarty should
flip the coin
and
choose a strategy). In a related context, Tullock (1992: 28) argues that the
feeling that because
of
the infinite regress there is actually no true solution is “... a correct
description of the game ...
Von
Neumann and Morgenstern (1944) purported to get out of this problem by
producing a mixed
strategy
for such games”.
10
This
may also have something to do with the fact that Morgenstern earlier (1941) had
penned a
vitriolic
attack on Hicks’ Value and Capital.
11
Specifically,
Debreu and Scarf (1963) showed that under perfect competition conditions,
letting
the
number of agents in the market tend towards infinitiy collapses the core of the
market game
into
the set of equilibrium prices.
12
But
only because they wished to draw on Nash’s use of Kakutani’s fixed point
theorem, and
could
see the strong similarity between proving the existence of competitive
equilibrium and
proving
the existence of equilibrium in an n-person, non-cooperative game.
13
Although
I cannot back this claim up by quotation data.
14
As
late as in 1979, Littlechild notes that “... for some time there has been a
state of disillusion
with
the whole approach. Some game theorists believe a feeling of optimism is
gradually
returning”
(1979: 145).
15
Indeed,
the probably first area that was completely and successfully conquered by game
theory
was
one in which at least the rhetorics concerns the formation of beliefs, rivalry
and competitive
22
struggle.
This area is industrial organization economics, where the SCP paradigm
associated with
Bain,
Mason, and others is now virtually completely defunct.
16
This
issue is a little bit tricky, depending somewhat on one’s understanding of
“Austrian” and
dating
of the socialist calculation debate. Both Wieser, Schumpeter and the early
Hayek admired
general
equilibrium economics, and Böhm-Bawerk essentially also constructed general
intertemporal
equilibrium models. The critique of general equilibrium theory in Austrian
thought
was
anticipated in Menger’s critical attitude towards Walras, but does not seem to
have been
carefully
articulated before Hans Mayer’s work (Mayer 1932). There is an argument that is
was
the
socialist calculation debate that finally made the Austrians realize how
different they were
from
the Walrasian orthodoxy that was slowly beginning to emerge as the dominating
core theory
in
the mind-nineteen thirties (e.g., Kirzner 1988). For the argument that internal
problems in
Austrian
business cycle theory were also important in this process, see Foss (1995).
17
This
is what Reder (1982) calls the “tight prior assumption”.
18
“Possibly”,
because the number of academic economists who worked on refining GE was
actually
quite small and there has continuously been a large number of mainstream
economists
who
haven’ been so charmed by the GE model, for example, older (pre-Lucas) Chicago
economists
such
as Stigler, Friedman, Coase, and others.
19
The
point that there are many research traditions in modern economics that
Austrians ought to
relate
to, and perhaps join forces with, is elaborated in Foss (1994).
20
See
also Machovec (1995) for a brilliant discussion and critique of the sway that
the perfect
competition
model held over the minds of economists in this century.
21
Although
admittedly the monopolist’s choice is in reality just as constrained as the
choice of an
agent
in competitive equilibrium. However, such is the nature of all (single-exit)
modelling.
22
It
is noteworthy, however, that a recent collection of papers on “market process
economics”
contains
a number of formal papers (Boettke and Prychitko 1998).
23
The
economic substance is usually provided in what formalists usually, and somewhat
pejoratively,
characterize as ”intuition” (a remarkably imprecise use of that word!), and
which
has
historically normally been put forward by non-formal economists.
24
A number
of attempts to add more behavioral realism in the form of bounded rationality
have
been
made (see Kreps 1990).
25
The
exception is, of course, constituted by evolutionary game theory, which, in
some
interpretations,
provide a justification for focusing on Nash equilibria (Weibull 1995). See
Aumann
and Brandenburger (1995) for a recent discussion of the “epistemic conditions
for Nash
equilibrium”.
26
Notice
that I am not here talking about game theory in general, but about “standard
game
theory”,
which is more less models with complete information and common knowledge. In
contrast,
game theory work by, for example, Sugden (1986) certainly successfully makes
sense of
the
notion of unintended consequences, as observed earlier.
27
In
many respects, Wieser was closer to the competitive equilibrium vision of
Walras and Pareto
than
Menger and Böhm-Bawerk.
28
For
example, a key point in both game theoretic contract theory (e.g., Salanié
1997) and in IO
(Krouse
1990) concerns the timing of actions, because final outcomes are often
crucially dependent
23
upon
this. Thus, in a contractual relation, the timing of payments may influence how
much effort
is
exerted.
29
Actually,
we need an article-length study of the “Austrian’ness” of Oskar Morgenstern.
Schotter
(1992)
is a first step in that direction.
30
This
is a game in which there is no conflict of interests, as, for example, when
players in a “state
of
nature” has to choose which side of the road to drive in.
31
At
the outset, the players have different descriptions of the game. For example,
they may both
think
of themselves as, for example, the row player.
32
The
point that game theory is much better equipped to come to terms with
institutions than
standard
neoclassical theory is made several times in Von Neumann and Morgenstern (1944)
(see
also
Morgenstern 1972; Schotter 1992).
33
Actually,
Shackle (1972) contains a critique of game theory that is essentially the same
as
Shackle’s
general critique of economic doctrines: game theory cannot accomodate human creativity
and
neglects surprises.
34
This
particular objection is not likely to have much success against game theory.
Game theorists
are
very much bent on essentialism and conceptual analysis.
35
They
are not completely clear here, but seem to mean that what the mind construct
can do shall
be
realistic in a broad sense: “An ‘understandable’ relation must be
understandable in the
structural
terms of commonse interpretation of everyday life. Hence the scientific
constructs must
be
consistent with, although not identical to, the mental constructs of
everyday life” (ibid.).