Interaction and markets
Alan Kirman
GREQAM
EHESS and Universite d'Aix-Marseille lll,
Institut Universitaire de France.
Economists do not like the idea of comparing the economy to an ants’
nest or to a
bee-hive. They are no doubt convinced that such organisations are in some sense
optimal but they are not convinced that the optimality is achieved in the same way as
it is in an economy or market. Thus, if you ask most economists what is the basic
question that concerns them they will probably answer that it is to understand what
the equilibrium of the economy or market that interests them is like, and whether it
entails an efficient use of resources. Yet there is a prior problem that intrigues many
people when they first come to economics and which is posed by the behaviour of
social insects. It is that of explaining how the myriad of disparate individual economic
activities, in a modern economy, come to be coordinated. Economic agents
constantly interact with each other in different ways and for different purposes and
somehow out of these individual interactions a certain coherence at the aggregate
level develops. Disappointingly economics has rather little to say about this. The
reason is that the basic paradigm in economic theory is one in which individuals take
decisions in isolation, using only the information received through some general
market signals, such as prices, to make their decisions. The standard model does not
deny that agents interact but, as Samuelson said, they only do so through the price
system. Indeed, a way of characterising the efficient markets hypothesis so pervasive
in the financial markets literature is to say that all information private and public is
aggregated in the price system. Thus no agent has any interest in searching for
information other than from prices. Direct interaction is not an integral part of market
behaviour according to this view.
In the standard model, all agents have the same information. The information
available is global and not local. Although we know from Jordan’ s result that
astonishingly little information is needed to achieve efficiency the description of the
way in which the mechanism functions is hardly realistic. Agents are isolated from
each other and if there are asymmetries in their information there is frequently no
discussion as to their origins. Consider another vision of the world in which
individuals function in a limited neighbourhood and most of their information comes
from those with whom they interact. Furthermore, their reasoning capacities are
limited and they adapt rather than optimise. Is it not possible that in such a world the
collective outcome has certain
desirable properties? What I have just described
corresponds very well to the situation in an ants’
nest or a bees’
hive. This is very
different from a world in which individuals are intelligent and calculating but are not
limited in their vision of the economy.
Economic agents do, in fact, communicate with each other and learn from each
other. They also infer information from the actions of others and, most importantly, in
most markets they trade with each other There is of course an approach, the game
theoretic one, which takes direct account of this. However this is at the opposite
extreme. Every player takes account of what every other player does and moreover
knows that the others do so. This leads to computational problems which mean that
only limited examples can be fully analysed and also to basic logical problems.
My position is that we need an approach which lies in between the standard model
and the full blown game theoretic model, but which allows for various forms of nonmarket interaction. There are moves in this direction but they are, as yet, few in
number, (see Glaeser and Sheinckman (2001).
Individual and Collective Rationality
Perhaps the easiest description of this view is to think of the economy as a complex
system where aggregate behaviour is determined by the complicated interaction
between individuals at the micro level. The analogies with physical, chemical and
biological systems are obvious. My idea is not however to develop a methodological
position along these lines. I want rather to argue that there are important lessons
about the way in which economies work which we can learn from the research in this
area. There are economic phenomena or structures, which emerge from these
interactive models, which are not readily obtained with more standard analysis.
Perhaps most importantly such models offer a useful way of looking at how market
structure and organization emerge. This sort of argument has been made with force
by Lesourne (1992).
One important concept, once one allows for direct interaction among agents, is that
macro behaviour cannot be thought of as reflecting the behaviour of a "typical" or
"average" individual. There is no simple direct correspondence between individual
and aggregate regularity. A simple empirical example of this is that of the behaviour
of agents on a market for a perishable product, fish. In Hurdle and Kirman [1994] we
showed that although the transactions of individuals, on this market, do not
necessarily reveal any of the standard properties of a demand curve nevertheless in
aggregate there is a nice downward sloping relationship between prices and
quantities transacted.
In many situations we see that collective behaviour may be “ rational” whereas that
of the individuals may not be so. In a series of public goods experiments it was
observed that the total contributions of the individuals converged towards the Nash
equilibrium. Yet examination of individual behaviour showed that it was far from being
the case that each individual wound up playing Nash. Collectively they achieved a
certain coherence in their behaviour but thiswa not due to the strict rationality of
each player. The same remarks can be made concerning the famous “ El Farol Bar
problem” introduced by Brian Arthur.
Bees of a certain type cool their nest by flapping their wings. However it is not true
that as the temperature rises they flap their wings harder. More bees join in. Thus the
right temperature is achieved because of the varying thresholds of reaction fo the
bees. Bees are either on or off with reapect to this behaviour. The individual
behaviour is very simple but the collective outcome is very sophisticated.
These are just examples, but suggest an important idea. Aggregation may, as
Werner Hildenbrand (1994) has suggested, generate structure and regularity. The
individuals involved may have a very limited view of some part of the economy but in
the large their activities may self-coordinate into well-defined aggregate behaviour.
Without making invidious comparisons one has only to think of the way in which the
activities of individual ants are coordinated into the organisation of the colony.
Different Forms of Interaction
Economic agents may interact in many different ways. Certain individuals may only
be able to trade with certain others; some agents may try to make inferences from
the activities of others. Some economic actors may only communicate with a subset
of the others. People may change their expectations as a function of the expectations
of the others with whom they are in contact.
A first approach to analysing this sort of problem is to stay within the standard
framework and to define a suitable sort of static equilibrium, which takes account of
interaction. The latter may be local or global, that is, in the first case agents will be
limited as to whom they have contact with, in the second agents may meet any other
agent. Many of the static search equilibria à la Diamond, for example, can be viewed
in this way. In this sort of model, however, the notion of equilibrium remains, as in the
standard model, a static fixed point. Agents still react to an anonymous signal, but in
this case it is the distribution of the prices of a certain good. In addition the only
stochastic element in this sort of situation is the random matching of the agents.
Yet much interaction in economic activity is stochastic in its nature and if we want to
go further in incorporating direct interaction into our economic models it seems to me
that we have to take this into account.
The first contribution in which the problem of stochastic interaction was explicitly
treated is that of Foellmer [1974]. He showed that if the characteristics of agents, for
example their preferences are random but dependent on those of others, the effect of
large numbers of agents is not enough to eliminate uncertainty at the aggregate level.
Many have argued that it is enough to look at the behaviour of the average agent
since the law of large numbers will wash out the effects of the random interactions
between agents. Foellmer showed that this is not true. Once again removing the
independence of agents has important consequences for the way in which micro
behaviour is related to aggregate phenomena. Recently Forni and Lippi (1996) have
shown how, in macro dynamic models, micro behaviour may have one characteristic
but at the aggregate level this is reversed. This is the case when individuals react to
idiosyncratic, but independent, shocks whereas they also react to common
exogenous shocks. At the aggregate level the individual shocks cancel out but the
interaction through the reactions to the common shocks remains.
This brings me to the idea of looking at the dynamic evolution of the economy
resulting from the interaction between agents. In this case one is interested in
knowing how the state of the system evolves over time and whether it settles down to
what might be thought of as some sort of equilibrium.
There are various examples of this sort of analysis. One is the pioneering work on the
diffusion of information done by Allen [1982]. Another is the adoption of technological
innovations as agents profit from the externalities of others having already adopted a
particular technique (see Arthur [1989] and David [1985]). The argument here is that
an a priori inferior technology may come to dominate a market, as in the case of the
QWERTY keyboard for typewriters.
Herd Behavioujr in Financial Markets
Another example and one of particular interest to those interested in finance, is the
sort of herd behaviour that may arise as agents are influenced by what other agents
do (see Banerjee [1992], Kirman [1993], Sharfstein and Stein [1990]) and indeed a
number of phenomena corresponding to Keynes' "beauty queen" contest can arise.
The most striking cases are those in which economic agents observe the actions of
others and infer information from those actions. This is an essential feature of the
way in which traders behave for example. What can happen in such a case is that
agents consider the information they have gained in this way as being of more
importance than their own. They will, then, no longer act on their own information and
it will never have an impact on the market. Not all information is aggregated, the
efficient market hypothesis breaks down and we have what is referred to as an
“ informational cascade” , (see Bickchandani et al (1992) and Chamley (2002)).
This seems a reasonable route to follow when one is seeking to explain “ bubbles” ,
for example, rather than to rely on more “ psychological” explanations which simply
attribute such phenomena to irrational behaviour, (see, Shiller (2000)) This raises
another important issue which receives little attention in the literature, the problem of
the agents’
horizons. Agents cannot be condemned for following trends if they are
going to be judged on their short term performance. It is not enough to be convinced
that the fundamentals are not in agreement with current prices if one is not sure when
the fundamentals will re-establish themselves. Thus interaction between agents with
very different horizons may have important implications for market behaviour.
A further problem is that of differences of opinion. In standard models where there is
uncertainty the usual way of achieving consistency is to assume that agents have
common and “ rational”
expectations. How then do we deal with the fact that
agents do, in fact, differ in their opinions and forecasts and that this is one of the
main sources of trade. An answer is to suggest that individuals may change their
opinion or forecast as a function of those other agents. In simple models of financial
markets such changes may be self reinforcing. If agents forecast an increase in the
price of an asset and others are persuaded by their view the resultant demand will
drive the price up therby confirming the prediction. Such models may generate
swings in opinions regime changes and “ long memory”
all of which are hard to
explain with standard analysis. An essential feature of these models is that agents
are wrong for some of the time, but, whenever they are in the majority they are
essentially right. Thus they are not systematically irrational. (for examples of this sort
of model see, Lux and Marchesi (2000), Brock and Hommes (1999) and Krrman and
Teyssiere (2002)).
An alternative view of viewing markets is in an evolutionary light. In this view
economic agents are continuously learning and changing their strategies. This is the
basis of the evolutionary games literature.. The number of agents who are identified
with successful strategies expands over time. Agents are typically matched randomly
with others in this sort of model but it is by no means always true that stable patterns
will develop, nor even if they do that they will correspond to socially optimal
outcomes. On eof the drawbacks of this type of analysis is that the set of possible
strategies is taken as given and unchanging. Thus although there is constant
interaction between agents, it is in a static setting. However, one of the interesting
feature of economics is that new strategies are constantly emerging. A rare exception
is the contribution of Lindgren (1991) who allows the possible strategies in a repeated
"prisoners' dilemma" game to evolve over time and shows that this radically alters the
nature of aggregate behaviour which continues to evolve and is occasionally
punctuated by periods of upheaval.
Local Interaction
While these models bring out the importance of interaction it seems to me that
models with local interaction are even more interesting, for they give much more
concrete form to the idea that since agents are limited to a set of neighbours with
whom they interact, changes will not affect all agents simultaneously but rather
diffuse across the economy. One particular feature of interest is that when agents are
not sure about whom they interact with, and make the wrong assumption about
whose behaviour affect them, they can be led into "self confirming equilibria". Thus
because of the imperfect perception by agents of local interaction, aggregate
phenomena will appear which would not occur if agents had full information, (see
Kirman (1983). What is intriguing is that in such situations the agents will believe that
they are right and will observe nothing to undermine their view.
If we are to talk about local interaction we have to specify who interacts with whom.
Typically agents in models of local interaction are thought of as being placed on a
lattice and interacting with their neighbours (see Durlauf [1990] , Benabou [1992],
Blume [1993] and Ellison [1993] and Brock and Durlauf (2001)). In this case one is
interested to know whether pockets or clusters with certain behaviour or
characteristics may form. The spatial connotation is by no means necessary however
and alternative structures of links can be considered (see Kirman, Oddou and Weber
[1986] and Ioannides [1990 and 1997]).
In all these models the important feature, from an economic point of view, of the
graph representing the links between agents is how connected it is. This will
determine how fast information diffuses and how quickly an epidemic of opinion or
behaviour will occur. Stochastic graphs become surprisingly highly connected as the
number of agents increases provided that the probability that any two individuals are
connected does not go to zero too fast. The dynamic evolution of the state of the
individuals linked in a graph like structure is particularly interesting and some of the
results from other disciplines (see Weisbuch [1990]) can be evoked in the context of
economic models.
Another interesting approach is to examine what happens when, although agents
modify their behaviour in the light of their own and their neighbours' experience, the
consequences of their behaviour may affect other agents further afield. Weisbuch et
al. [1994] for example show how agents may chose polluting or non polluting devices
from local experience but their choice may result in pollution which diffuses widely.
The consequence of this may be rather sharp division into areas in which all the
agents have adopted one type of device while in another area the alternative device
will be used.
As I suggested at the outset the most interesting challenge in this area is to study not
just the behaviour or "states" of individuals who interact in a general or local way but
also the evolution of the communications graph itself. Durlauf [1990] introduces
something of this sort when he considers not the network itself as changing but rather
that agents may choose when to place themselves in the network, and this recalls an
older model of neighbourhood preferences due to Schelling. Krugman's (1991,1994)
modelling of geographical phenomena also has this flavour.
More directly Vriend's [1995] contribution presents a first step to simulating a model
in which either the links themselves or the probability that they will be used over time
evolve. He constructs a market in which buyers learn when to shop and firms learn,
from experience, when to buy. In this model firms sell indivisible units of a
homogeneous good, the price of this good is fixed and agents demand at most one
unit. Nevertheless it is particularly interesting to note the development and
persistence of a non degenerate size distribution of firms even though all firms are
identical to start with. Furthermore some buyers always return to the same store
whilst others continue to search. There is empirical evidence for this sort of division of
activity both on product and in financial markets. We have continued this sort of work
in a more general setting, (Kirman and Vriend (2001)) and find a number of
interesting macro-phenomena arising within a framework in which agents follow
extremely limited rules and simply reinforce the probability of using those which are
most successful. We have also developed, (Weisbuch et al. (2000)), a theoretical
framework within which to analyse the sort of phenomena just discussed and in
particular the development of links between agents in a market. We show that
markets may either "self organise" strongly or may remain "disorganised", and the
crucial factor will be the extent to which agents behaviour is reinforced by their
behaviour. The transition from "organisation" to "disorganisation" is surprisingly
abrupt. Data from the Marseille fish market confirm the theoretical results. This is a
very specific example but the explanation of theformation of trading links and groups
such as those that have often been observed even on supposedly anonymous
markets is surely of interest.
There are very few other theoretical economic models that consider the evolution of
the network itself. An early model of Whittle (1986) examined the emergence of
markets. Ioannides (1997) deals with the evolution of stochastic graphs but only
deals in passing with the endogenous evolution of the links. One example is that of
Stanley et al. [1994]. They develop an evolutionary model of the repeated prisoners
dilemma in which, as agents learn from experience, they may refuse to play with
certain others and one can examine the distribution and local concentration of
strategies that develop. Another is that of Mailath et al. (1995) where individuals can
choose whom to interact with.
To return to one of the remarks made at the outset, those who pursue a game
theoretic approach have developed models of strategic network formatin in which
people deliberately and consciously choose the network they want to belong to, ( see
Jackson and Wolinsky (1996) and Bala and Goyal (2000)).
A fascinating example of the role of networks is by Guriev et al.(1995). They study
the impact of "infrastructure" on the formation of trading networks and show how
under different assumptions about the cost of developing lijnks very different dynamic
aggregate behaviour can develop. This can vary from a nearly perfectly competitive
situation with few trading intermediaries to one with many traders and periodic bursts
of shortage. Very few of these models have been checked against data though there
are some such as one slightly eccentric example which is that of McLean and
Padgett (1996) who study evidence on the trading networks in mediaeval Florence.
Despite the limited amount of work done on it, it seems to me that the question of
how economic networks evolve is one of the most important if we are to begin to
understand how markets come to be organised. I believe this question should be
given much greater attention and that the tools are available to study it. Curiously
almost all the models I have cited can be reduced to studying how probability
distributions evolve over time. The particular mapping will depend essentially on the
features of the economic model one wishes to study but the underlying framework is
the same.
Conclusion
In conclusion models which take account of the direct interaction between agents
allow us to provide an account of macro phenomena which are caused by this
interaction at the micro level but are no longer a blown up version of that activity.
Furthermore the sort of behaviour that may occur at the aggregate level is much
richer than in standard models. Bubble-like phenomena in financial markets,
persistence of inferior technologies, spatial variability of activities or of income levels
are among the phenomena that arise naturally in this type of analysis. However
perhaps the most interesting of all is the avenue opened up towards an
understanding of how market structure may emerge endogenously. If this is to be
pursued successfully, I would strongly urge people to build up more data sets for
specific markets. Lastly I would add that I am convinced that the sort of approach
adopted in the "artificial life" literature in which individuals are endowed with rather
limited reasoning and calculating capacities, and structure emerges as they learn
from experience, is the appropriate one. This seems to me much more promising
than models based on individuals capable of maximising and in so doing of solving
extremely complex problems. Individuals in economies are not blind and without
purpose or intent as are ants, but they function is a very limited part of the economic
environment and are at best aware of a part of that environment. Worse, they make
mistakes and in most standard models this is not allowed for. Yet, together they may
coordinate on quite sophisticated solutions to the allocation problem. Put alternatively
collective rationality is very different from individual rationality and it is a mistake to
talk of market behaviour as that of an individual. Complexity seems to me to be a
property of economic organisations not of economic individuals.
References
Allen B. (1982), "Some stochastic processes of interdependent demand and technological
diffusion of an innovation exhibiting externalities among adopters", International Economic
Review, Vol. 23, n. 3, October, pp. 595-608.
Arthur W.B. (1988), "Self-reinforcing mechanisms in economics", in The Economy as
an Evolving Complex System, Anderson P.W., Arrow K.J. and D. Pines (eds.),
Redwood City, CA, Addison-Wesley, pp. 9-32.
Arthur W.B. (1989), "Competing technologies, increasing returns and lock-in by
historical events", Economic Journal, IC, pp. 116-31.
Bala V and S Goyal (2000), « A Non-Cooperative Model of Network Formation »,
Econometrica, vol.68, pp. 1181-1230
Banerjee (1992), "A simple model of herd behaviour", Quarterly Journal of
Economics, vol. 108, 797-817.
Benabou R., (1996), "Heterogeneity, Stratification and Growth: Macroeconomic Implications
of Community Structure and School Finance", American Economic Review, vol. 86 pp. 584609
Bikhchandani S., Hirschleifer D. and Welch I. (1992), "A Theory of Fads, Fashion, Custom
and Cultural Change as Informational Cascades", Journal of Political Economy, vol.
100. pp. 992-1026.
Blume L. (1993), "The statistical mechanics of strategic interaction", Games and
Economic Behavior, 5, pp. 387-424.
Brock W., and S. Durlauf., (2001a), "Discrete Choice with Social Interactions"
Review of Economic Studies, vol.68, pp.235-260
Chamley C (2002), Rational Herds, Cambridge, Cambridge University Press.
David P. (1985), "Clio and the economics of QWERTY", American Economic Review,
proc. 75, pp. 332-7.
Durlauf S. (1990), Locally interacting systems, coordination failure, and the behaviour
of aggregate activity", Working Paper, Stanford University.
Ellison G. (1993), "Learning, local interaction and coordination", Econometrica, vol.
61, September, pp. 1047-1072.
Foellmer H. (1974), Random economies with many interacting agentsÔ, Journal of
Mathematical Economics, vol. 1, 1, March, pp. 51-62.
Glaeser E and Scheinkman J, (2001) “ Non-Matket Interaction” , NBER working
paper no. W8053, NBER Cambridge
Guriev S., I Pospelov and M Shakhova (1995), "Self-Organization of Trade Networks
in an Economy with Imperfect Infrastructure", Mimeo, Computing Center of The
Russian Academy of Sciences, Moscow.
Haerdle W. and A.P. Kirman (1994), "Non classical demand: a model-free
examination of price quantity relations in the Marseille fish market", Journal of
Econometrics, vol. 67,
Ioannides Y.M., (1997), "Evolution of Trading Structures", in The Economy as an
Evolving Complex System II, eds., W. B. Arthur, S.N. Durlauf, and D.A. Lane,
Addison Wesley, pp. 129-167
Ioannides Y.M. (1990), “ Trading uncertainty and market form” , International
Economic Review, vol. 31, 3, August, pp. 619-38.
Jackson M and A Wolinsky (1996), A Strategic Model of Social and Economic Networks”,
Journal of Economic Theory, vol. 71, pp.44-74
Kirman A.P. (1983) "Mistaken beliefs and resultant equilibria", in Individual
Forecasting and Collective Outcomes, R. Frydman et E. Phelps (eds.), Cambridge
University Press, 1983.
Kirman A.P. (1993), "Ants, rationality and recruitment", The Quarterly Journal of
Economics, vol. 108, February, pp. 137-156.
Kirman A.P. (1994) "Economies with interacting agents", Working paper 94-05-030,
Santa Fe Institute, Santa Fe, NM.
Kirman A.P., C. Oddou and S. Weber (1986), "Stochastic communication and
coalition formation", Econometrica, vol. 54, January, pp. 129-138.
Kirman A P and G Teyssiere (2002) “ Micro-economic Models for Long Memory in
the Volatility of Financial Time Series”
in PJ J Herings, G Van der Laan and A J J
Talman (eds), TheTtheory of Markets, pp. 109-137, North Holland, Amsterdeam
Kirman, A.P., & Vriend, N.J. (2001). Evolving Market Structure: An ACE Model of
Price Dispersion and Loyalty. Journal of Economic Dynamics and Control, 25, Nos.
3/4, 459-502
Lesourne J. (1992), The Economics of Order and Disorder, Clarendon Press, Oxford.
Lindgren K. (1991), "Evolutionary Phenomena in Simple Dynamics", in Artificial Life ll,
C.G.Langton, C. Taylor, J.D. Farmer, & S. Rasmussen (eds), Addison-Wesley,
Redwood City, CA.
Mailath G, L Samuelson and A Shaked (1994), "Evolution and Endogenous
Interactions". CARESS Working Paper no. 94-13, University of Pennsylvania.
Mclean P.D and J.F.Padgett (1996), "Was Florence a Perfectly Competitive Market?:
Transactonal Evidence from the Renaissance, Theory and Society (forthcoming).
Sharfstein D. S. and J. C. Stein (1990), "Herd behaviour and investment", American
Economic Review", vol. 80, 3, pp. 465-79.
Shiller R (2000), Irrational Exuberance, Princeton, Princeton University Press.
Stanley E.A., D. Ashlock and L. Tesfatsion (1994), "Iterated prisoner's dilemma with
choice and refusal of partners" in Artificial Life III, C.G. Langton (ed.), Santa Fe
Institute Studies in the Sciences of Complexity, proc. vol. XVII, Addison-Wesley.
Vriend, N.J. (1995). Self-Organization of Markets: An Example of a Computational
Approach. Computational Economics, 8, No. 3, 205-231
Weisbuch G. (1990), "Complex System Dynamics", Addison-Wesley, Redwood City,
Ca.
Weisbuch et al. (1994), "Dynamics of economic choices involving pollution", Working
paper 94-04-018, Santa Fe Institute, Santa Fe, NM.
Weisbuch, G., Kirman, A., & Herreiner, D. (2000), "Market Organisation and Trading
Relationships , Economic Journal, 110 pp.411-436
Whittle P. (1986), "Systems in Stochastic Equilibrium", John Wiley and sons, New
York.