EUROPEAN UNIVERSITY INSTITUTE, FLORENCE
DEPARTMENT O F ECONOMICSF
o r k i n g p a p e r n o. 88/351
; AND MARKETS byAlan
K I R M A NBADIA FIESOLANA, SAN DOMENICO (F I)
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
All rights reserved. No part of this paper may be reproduced in any form without
permission of the author.
(C) Alan Kirman Printed in Italy in June 1988 European University Institute
Badia Fiesolana - 50016 San Domenico (Fi) -
Italy © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
ON ANTS AND MARKETS 1:
A lar. P. KIRMAN
European University Institute 50016 San Domenico di Fiesoie. Itaiv
Man has long been intrigued by the behaviour of social
insects and the rationale for their apparently complicated
behaviour. The observed complex patterns may sometimes be
derived from rather simple individual behavioural rules and
the interaction between the individuals involved. This
paper describes some counterintuitive phenomena observed in
certain species of ants, provides a simple mathematical
model to explain these phenomena and then suggests how these
phenomena may be reinterpreted to explain market behaviour
which seems to correspond to many observed features and yet.
is difficult to explain with standard models. Whilst the
paper probably generates more questions than answers. it
suggests an underlying mechanism very different from those
incorporated in more conventional models, which may prove a
useful way of looking at certain market features. In
particular the model used generates endogenous market,
fluctuations which, whilst not chaotic in the standard
sense, exhibit certain features which seem to coincide with
some empirical behaviour.
Ants: The empirical evidence
j I an greatly indebted to Hans Follmer who provided the basic insight as to the nature of the stochastic process
involved here. We are pursuing joint work on the issues
^ raised in this paper. X am also grateful to Michael
Woodford for his helpful comments. The usual disclaimers apply. 1 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
In a recent article Pasteels et al (1987) describe the
following phenomena:
Two identical sources of food piles. A and B. were
placed near to an ants' nest and were constantly replenished
so that they remained at the same level. When an ant finds
one of the sources he returns with food to the nest and lays
a chemical trail which increases the probability that
another ant emerging from the nest and searching
stochastically will find that pile. Since both heaps were
always found and exploited, the natural question to ask is
how did the ants distribute themselves between the two
heaps. Instead of finally settling, as one might have
expected, to an equal concentration at each heap the ants
would be heavily concentrated on say pile A and then there
would be a sudden switch to heap B and this switch would
occur from time to time. Pasteels et al (1987) constructed a
model of the ants' behaviour which reduces to a system of
differential equations for which the numerical solution gave
two steady states when the number of ants was large enough.
The two solutions are asymmetric in that each involves a
large proportion of ants feeding at one pile and a small
number at the other. Although such a model would explain
the asymmetric division of the ants it would not explain how
a switch in the intensity of exploitation from one pile to
the other would occur as does the model presented here.
For economists two remarks made by the entomologists in
question (Pasteels et al 1987) are of particular interest.
2 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
"Without falling into naive anthropomorphism, the
study of social insects has greatly benefitted from
distant analogies with human behaviour and economics"
and they also remark in connection with the stochastic
nature of individual behaviour:
"However it is remarkable that a mathematical model
based on these simple premises is able to generate
the coherent collective behaviour observed in the
experiments. We do not believe that more classical
approaches, such as a reductionist analysis of
communication or models based on optimisation theory
could have achieved this goal".
The economist' objection to the second observation must
be that there is something less than coherent about a
society which splits its resources between two identical
sources and in fact has some "lost ants" who find neither.
The defense is that the behaviour involved is efficient in
nature where there is always a likelihood of a food source
drying up and therefore society must always be on the
lookout for new sources. Presumably if the sources were
replenished over a sufficiently long period and there were
some learning 2 ) there would eventually be complete
concentration on the productive sources. Nevertheless as
our model shows the concentration would be asymmetric.
We will take here as the major features of our model
interaction and stochastic "recruiting" and try to reverse
2 Paradoxically Pasteels et al (1987b) in another paper look at the learning problem but consider it at the purely
individualistic level. 3 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
the trend observed by the entomologists by applying evidence
from insects to human behaviour.
A . s i m p l e f o r m a l , m o d e l
First we describe a simple mathematical model in which
individuals (ants) are recruited to one of two sources,
or as another interpretation to anticipate what follows,
there are two prevalent views in the world and when two
individuals with different views meet there is some
probability of one of them being converted to the other's
v i e w .
More formally, consider N (ants) people belonging to
one of two groups. The state of the system is defined as
the number of (ants) people k in group 1 .
i.e. k £ (0, 1, --- N)
Now the dynamics of the system are given by the following.
Choose one person at random then choose another. Let the
first be converted to the second’s group with probability l-£.
(He will otherwise change group with probability -§7 .
In a finite group the importance of this is obvious). The
pfocess may then be described as follows.
+
1
With p r o b a b i l i t y (1-;;) ( f + (1 - £ ) “ T )y/l N 2 N-l
(1 ) k
^ k - 1 with p r o b a b i l i t y ^ ( f + (1 - £) ^ ^ )
N 2 N - l
There are two special cases:
a) £ = 1 (no interaction, the first person chooses his
group by flipping a coin). This is the Ehrenfest urn model
with an equilibrium distribution which is binomial.
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
n
(k = 0, ...n) (k)
b) £ = 0 (total interaction, the first person moves to the
second’s group I. In this case the state k performs a
martingale with final absorption in k = 0 or k = N. with
Prob [absorption in k = N | initial state =kQ J = _£
In general the eouillbrium distribution p(k), (k = 0,
...n) of the Markov chain P (k, A. ) defined by (1) is
defined by
p(k) = I 1>U) W
1=0 ,.. .n
,c-V*C \
and can be explicitly calculated via the detailed.balanced
condition p(k) P(k, l) = ti(i) P ( i , k ), i . e . p(k) •“o p(0) ii (k) ji(k-l) ii(l) u(0) " ci( aiil 1 + t 1 ii(0 ) i=i 11 (k) n(k-l) ii (1 ) . . p ( i - l ) ) where 5 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
u(k-t-l) _ P(k - k+IL p(k) P0<+1 - M
( L -
5
) (f
(1
~ c)
>
( § + (1-eH1 * n=I
))-Now let us look at the asymptotic form when N-?*> and = M
for some OC > 0 . Let x =-^£[0. T\
When N is large p can be approximated by a distribution on
the interval [Jo, l] with density fix). Thus for N large we
have. f- -i /£ '■ V (k+l) - V (k) ^ f (N + N) - f(N j p(k) ~ 1/N f (k) ^ N j f’ lx)
But as N — ? 00 the right hand term is just '
Furthermore as S - ? 1® we have assumed Therefore we
have
f'(x) _ (j*-l)(l-2x)
f(x) X (1-x)
and that:
f is the density of a symmetric Beta distribution, l.e.
fix) = const, x**'"* ll-x) " - ' 1_____
The shapes of the distributions for different values of
£ are illustrated in figure 1. The time evolution of the
state x for N=50 and different values of £ is illustrated
in figure 2 . © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
Equilibrium.distribution for the model with state space £o.
1 ...nJ respectively , 1/N... 1^ with different.
values of £. and N = 1 0 0 .
Figure 1.
It is of interest to note that this is also related to
Polya's urn model a classical model for contagious effects,
which evolves as follows: Two groups of (people) ants, with
s ants each,start at time t = 0 and then at period t+l,c new
ants arrive, meet one randomly chosen ant from the old
population and follow it to its group.
The state at time t of the process, i.e. k ants in
crowd no. 1 changes to ktc with probability --- . The
2s + c . t
proportion of ants in crowd no. 1 which is^-t- converges
c . t
almost surely to a limiting value which has a Beta
s distribution with p a r a m e t e r - . 7 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
n « 50 epsilon = .001
Time evolution of the state x = "# ants in crowd No.i"
for n = 50, with starting value x = 25, for
e = .001, with
y
- corresponding equilibrium distribution.e = 0.9 , with | | = corresponding equilibrium distribution.
Figure 2 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
Some, observations fin...foreign-exchange markets
The first question. it we are to apply the model
developed above, that is natural to pose, is to what extent
are people in financial markets, tor example, influenced by
communicating with each other'? Do they not simply observe
market signals as a large part of the literature would have
us believe? If this were the case, the very basis on which
the model presented here is founded would be undermined.
However there is accumulating evidence that a great deal of
information is transmitted in this way and that, trading in
particular shares may often be prompted by a conversation
with another trader. Shiller and Pound ( 1 9 8 6 1 in a recent
article give substance to what is a long-standing feature of
market lore. Interestingly enough they explicitly refer to
the epidemic phenomenon and cite such standard texts on this
subject as Bailey (1975) and Kermack and McKendrick (1927).
The second question is to what extent does the market
reflect empirical features which would cast doubts on
existing explanations. Goodhart (1987) putting together
empirical evidence and knowledge of institutions points out
many of the weaknesses of existing theoretical models.
"Overshooting" is rarely observed and the responsiveness to
shocks is muted, in particular the impact of "unanticipated"
interest rate changes on spot exchange rates was
undetectable, the random walk with its persistence cannot be
easily rejected for nominal spot foreign exchange rates for
example, but seems to correspond to shorter rather than to
longer term views.
9 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
Goodhart (1987) is led to the belief that, the market
reflects a fundamental tug-of-war between two groups of
individuals, those who extrapolate and those who believe
that "fundamentals" play a determining role. A possibility
is that individuals are themselves schisophrenic, adopting
the extrapolatory view for their short term transactions and
the fundamentalist point of view for their longer term
positions. We shall take a simpler point of view and adopt
a model derived from one of Frankel and Froot (1986) in
which two views are held by individuals. In their model
actual trades are made by portfolio managers who attach
weights to the two different market views prevailing,
changing these weights in such a way as to forecast
correctly the current changes. But as they say:
"In any case one could interpret the two groups as
taking positions in the market directly rather than
merely issuing forecasts for the portfolio managers
to read".
Indeed Figlewski (1978, 1982) considers a model in which the
private information or views of individuals are transmitted
to the market through the market price and these views are
weighted by the relative wealth of the individuals.
In our model the important point is that agents change
their views by discussing with others whom they meet at
random. Now a problem raised by Michael Woodford 3) is that
3 In private correspondence. He suggests an alternative model in which agents of the two types are in fixed proportions and their demand is derived from a utility
function of the mean and variance of wealth. This model has
interesting features but involves individuals having fixed views as to the variance of future spot prices which would not be consistent with our model.
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
at. first, glance the process of conversion from one type to
another does not seem to be related to how the individuals
of each type are faring. In fact if there are many agents
of one type in the market, the probability of being converted
to that type is quite high. However, since these agents
dominate, the market reflects their view, and to maintain
the other view is losing behaviour. Thus there is a close
relation between conversion to a type and the fact. that, that
type’s view is economically correct. What is very important,
to note is that when there are large numbers of agents
plays almost no role in the conversion, the dominant part of
the probability is the relative size of the popoulation.
Thus it is the prevailing view that matters rather than
epsilon and this makes economic sense. We now give the.
details of our model.
A simple model of exchange rate determination
Modifying Frankel and Froot’s (1986) model as
suggested we consider a model in which there are two types
of agents. Firstly there are "fundamentalists" f who
believe that the change in the exchange rate st at time t
will tend to bring it back to an underlying equilibrium s
and whose forecast change is expressed by
A
3[+1
» V(S - Sfc)and secondly there are "chartists" who extrapolate naively
11 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
^t+l ” st ■ st-l
The “market, view" cari then be expressed as
* s t + l = " t “ t + l + (1 - w =t + l
where if k is the number of and there are N agents, then
fundamentalists in the market
The dynamics of kt. are given as described before by the
random meeting of agents.
The market actually evolves as follows:
ill n
s t = CASt + l + 2t
where Zt is some index of fundamental economic variables.
Frankel and Froot justify this model in different ways but
of course have a different dynamic for w+ . If we solve this
simple model and assume "rationality',' zt = s we obtain
(£) Sj. = [l+cwtV - c+cwt]-1 [Cltcw t V) s - c ( l - w , J st - 1 ]
Looking at the simple case in which c = 1, which depends
naturally on the underlying model, it is clear that i f ( l -
wt ) J(l + V) wtj - 1 > 1 the system becomes unstable.
Precisely this happens when the model is simulated as
can be seen in figure 3. It remains close to s for a long
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
Fundamentalists and Chartists,
Figure 3
time and then explodes. However, it is important to note
that the way in which the market evolves is highly dependent
on the number of meetings that take place between each price
change. The stability of the process is closely related to
this and it is interesting to reflect on the consequences of
the change from periodic fixing of prices with an opportunity
for discussion between price fixings to a system with
"continuous" price changes.
13 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
In fact, although our system "explodes" it would
eventually return to the fundamentalist equilibrium and
would thus exhibit the creation and extinction of bubbles.
The size and duration of these bubbles depends essentially
on the relative frequency of meetings and price changes.
Some intuition as to the evolution of s^ with can be
derived from looking at the derivative.
This can be contrasted with Frankel and Froot’s results
in that they have to introduce a further feature to induce
the eventual collapse of a bubble, whereas, in our case, the
evolution of w t guarantees this.
An alternative model is one in which there are two
types of fundamentalists believing respectively that the
exchange rate will return to i i , or s z .
In this case we have
__ t = _ [l+CW V - C + C W t 3wt T -]"2 [cv+c] ai+cwtv) s-c(l-w) V l + [1+CW,.V - c+ c w t l 1 [CVS + and we obtain ri(sl " st) + (1 - w) (S2 - st) 14 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
Now if we let. c = 1 and s
we obtain
st = [1+ w ^ + ( l -w t ) v 2] 1 (wt V s + ( ( l - w t ) v2 + i2
Now given the stochastic process governing w^. we can examine
the evolution of st and compare it with the results of
simulations in the previous case. This is illustrated in
figure 4.
Two Fundamentalists.
Figure 4 15 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.There is movement between the two equilibria and visual
examination would suggest the existence of "regimes" and
rapid shifts from one to the other. As mentioned before the
relationship between the frequency of meetings and of price
fixing plays a significant role in determining the pattern
of the exchange rate over time.
In this case the movements of the exchange rate are
characterised by shifts from one regime to the other whilst
in the first case the exchange rate remained at a given
level, then is characterised by a period of explosive
activity before returning to that level.
A different approach would be to suggest that people
appreciate that when their views are minority ones, markets
will not reflect these views. Thus, although having their
own opinions, they behave in line with the prevailing view.
However when the percentage of people agreeing with them
rises, they begin to anticipate a market change and switch
their behaviour. This would lead to more dramatic changes
in market prices than those in the model above, in which
people always behave according to their own views.
In this paper we have provided an account of a
mechanism which may be useful in explaining some features of
markets which seem to defy simple theoretical analysis of
the standard type. Here the important features are the
existence of different views of the market, stochastic
16 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
encounter between the individuals in the market and the
possibility of changing view. A natural question is why do
individuals change view so radically and not progressively.
In our second example the answer is clear. If the market
fluctuates between two levels and spends very little time at
intermediate values, the individual must forecast either the
high rate or the low rate and it never makes sense to
forecast some intermediate rate. The essential problem for
the agent is to anticipate the switch between regimes.
Finally it is worth underlining again the simple
coherence of the model. When one view predominates, the
evolution of the market reflects that view, and thus
justifies those holding it. This situation, as is only
reasonable, corresponds with a high probability of the
minority being converted to the prevailing view. Thus
although conversion is stochastic, the probability of being
converted to a view is dependent on how accurate that view
of the market i s .
A particularly interesting problem raised by the model
is that of the relationship of the number of encounters
between price changes to the stability of the evolution of
prices.
However the essential lesson to be learned here from
the behaviour of ants is the importance of individual
interaction and its consequences for the aggregate behaviour
of the system. Whilst this problem preoccupies other
scientists and social scientists it is one to which
economists tend only to allude.
17 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
References
Bailey. N .T .J .. f19751 The Mathemati,ca1 Theory of Infactioug
Diseases. London. Griffith.
Denenbourg J.-L., S. Goss, J.M. Pasteels, D. Fresneau and
J.P. Lachaud (19871 "Self organization mechanisms in ant
societies (II): Learning in foraging and division of
labour", in J.M. Pasteels and J.-L. Denenbourg (eds.). Fro®
Individual to._Collective___ Behaviour_in ,Social__ Insects,
Birkhauser, Basel.
Figlewski S. (1978) "’Market efficiency' in a market with
heterogeneous information". Journal of Political_.Economy,
v o l . 8 6 , pp. 581-597.
Figlewski S. (1982) "Information diversity and market
behaviour", Journal_of.Finance. p p . 87-102. March.
Frankel J. and K. Froot (1986) "The dollar as a speculative
bubble: a tale of fundamentalists and chartists". National
Bureau of Economic Research Working Paper n o . 1854.
Goodhart C. (1987), "The foreign exchange market: a random
walk with a dragging anchor", London School__q£_.Economics
Fin.anc.ial Markets GrouE_Warking.Paper no. l.
Kermack, W.O. and A.G. McKendrick (1927) "Contributions to
the mathematical theory of epidemics", Proceedings _0.f__the
Royal....Society, p p- 700-21.
Pasteels J.M., J.-L. Denenbourg and S. Goss (1987a) "Self
organization mechanisms in ant societies (I): Trail
recruitment to newly discovered food sources", in J.M.
Pasteels and J.-L. Denenbourg (eds.), From__ Inhiyid.U.al__tC
Shiller R.J. and J. Pound (1986) "Survey evidence of
diffusion of interest among institutional investors",
, Birkhauser, Basel. no. 1851. © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
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Paolo SICONOLFI
Alfred STEINHERR
David CANNING Optimal Monetary Policy in an Economy without a Forward Market for Labour
Joerg MAYER Intervention Mechanisms and Symmetry in the EMS
Keith PILBEAM Exchange Rate Management and the Risk Premium © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
5
-88/348: Milica UVALIC The Investment Behaviour of the Labour- Managed Firm: an econometric analysis
88/351: Alan P. KIRMAN On Ants and Markets
88/352: Gianna GIANNELLI Labour Demand, Pricing and Investment Decisions in Italy: An econometric Analysis
88/353: Niall O'HIGGINS The Progressivity of Government Taxes and Benefits in Ireland: a comparison of two measures of redistributive impact
Spare copies of these working papers and/or a complete list of all working papers that have appeared in the Economics Department series can be obtained from the Secretariat of the Economics Department.
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
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EUI Working Papers are published and distributed by the European University Institute, Florence.
A com plete list and cop ies of Working Papers can be obtained free of charge - depending on the availability of stocks - from:
T h e P u b lic a tio n s O ffic e r E u ro p e a n U niv e rsity Institute
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© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
PU B LIC A T IO N S OF T H E E U R O P E A N U N IV ER SITY IN STITU TE
T o T h e P u b lic a tio n s O ffic e r E u ro p e a n U n iv e rsity Institute B a d ia F ie so la n a
I - 50016 San D o m e n ico di F ie s o le (FI) Italy
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□ a com plete list of EUI Working Papers □ the following EUI Working Paper(s):
Author, title: Date: Signature: © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
21
PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE JUNE 1988 87/300: A. ELZINGA, P. NABER,
R. CIPPOLLINI, F. FACCIOLI, T. PITCH
Decision-Making About Girls by the Criminal Justice System in Holland and Italy
87/301: S. LEES, J. SHAW, K. REISBY
Aspects of School Culture and the Social Control of Girls
87/302: Eleanor MILLER, Rosa ANDRIEU-SANZ and Carmen VAZQUEZ ANTON
Becoming a Teenage Prostitute in Spain and the U.S.A.
87/303: Mary EATON and Lode WALGRAVE
A comparison of crime and its
treatment amongst girls in Britain and Belgium
87/304: Annie HUDSON Edna OPPENHEIMER
Towards an effective policy for delinquent girls
87/305: G. VAN DER LAAN and A.J.J. TALMAN
Computing, Economic Equilibria by Variable Dimension Algorithms: State of the Art
87/306: Paolo C. GARELLA Adverse Selection and Intermediation 87/307: Jean-Michel GRANDMONT Local Bifurcations and Stationary
Sunspots 87/308: Birgit GRODAL/Werner
HILDENBRAND
Income Distributions and the Axiom of Revealed Preference
87/309: Eric PEREE/Alfred STEINHERR
Exchange Rate Uncertainty and Foreign Trade
87/310: Giampaolo VALDEVIT American Policy in the Mediterranean: The Operational Codes, 1945-1952 *
87/311: Fede r i co ROMERO United States Policy for Postwar European Reconstruction: The Role of American Trade Unions *
87/312: Pietro REICHLIN Output-Inflation Cycles in an Economy with staggered wage setting
87/313: Neil KAY,
Jean-Philippe ROBE and Patrizia ZAGNOLI
An Approach to the Analysis of Joint Ventures *
87/314: Jane LEWIS Models of Equality for Women: The Case of State Support for Children in 20th Century Britain
rWorking Paper out of print
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
22
PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE JUNE 1988 87/315: Serge NOIRET Nuovi motivi per studiare i meccanismi
delle leggi elettorali. Una
riflessione metodologica a proposito della legge del 1919 in Italia 87/316: Alain GOUSSOT Les sources internationales de la
culture socialiste italienne à la fin du 19e siècle et au début du 20e siècle. Problèmes de la composition de l'idéologie du PSI et ses rapports avec la circulation des idées en Europe
87/317: Eamonn NOONAN Württtemberg's exporters and German protection, 1931-36
87/318: Jean-Pierre CAVAILLE Theatrum Mundi. Notes sur la théâtralité du Monde Baroque. 87/319: Peter RAPPOPORT and Segmented Trends and Nonstationary
Lucrezia REICHLIN Time Series
87/320: Douglas GALE A Strategic Model of Labor Markets with Incomplete Information
87/321: Gianna GIANNELLI A Monopoly Union Model of the Italian Labour Market
87/322: Keith PILBEAM Sterilization and the Profitability of UK Intervention 1973-86
87/323: Alan KIRMAN The Intrinsic Limits of Modern Economic Theory
87/324: Andreu MAS-COLELL An Equivalence Theorem for a Bargaining Set
88/325: Angela GROPPI "La classe la plus nombreuse, la plus utile et la plus précieuse".
Organizzazione del lavoro e conflitti nella Parigi rivoluzionaria.
88/326: Bernd MARIN Qu'est-ce que c'est "Le Patronat"? Quelques enjeux théoriques et observations empiriques
88/327: Jean BLONDEL Decision-Making Processes, Conflicts, and Cabinet Government
88/328: Ida KOPPEN The European Community's Environment Policy.
From the Summit in Paris, 1972, to the Single European Act, 1987
îWorking Paper out of print
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
23
PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE JUNE 1988
88/330: Milica UVALIC
88/331: David CANNING
88/332: Dalia MARIN
88/333: Keith PILBEAM
88/334: Hans Ulrich Jessurun d'OLIVEIRA
of Austria
"Shareholding" in Yugoslav Theory and Practice
Convergence to Equilibrium in a Sequence of Games with Learning
Trade and Scale Economies. A causality test for the U.S., Japan, Germany and the UK
Fixed versus Floating Exchange Rates Revisited
Die EWG und die Versalzung des Rheins
88/335: Felix Fitzroy and Kornelius Kraft
Piece Rates with Endogenous Monitoring Some Theory and Evidence
88/336: Norbert LORENZ
88/337: Domenico Mario NUTI
88/338: Pietro REICHLIN and Paolo SICONOLFI 88/339: Alfred STEINHERR
Die Ubertragung von Hoheitsrechten auf die Europaischen Gemeinschaften - verfassungsrechtliche Chancen und Grenzen einer europaischen Integration erlautert am Beispiel der
Bundesrepublik Deutschland, Frankreichs und Italiens
-On Traditional Cooperatives and James Meade's Labour-Capital Discriminating Partnerships
Government Debt and Equity Capital in an Economy with Credit Rationing The EMS with the ECU at Centerstage: A proposal for reform of the European Exchange rate system
88/340: Frederick VAN DER PLOEG
88/341: David CANNING
88/342: Gunther TEUBNER
88/343: Jean BLONDEL
Monetary and Fiscal Policy in Interdependent Economies with Capital Accumulation, Death and Population Growth
Optimal Monetary Policy in an Economy without a Forward Market for Labour
"And God Laughed..."
Indeterminacy, Self-Reference and Paradox in Law
Ministerial Careers in Western European Governments
:Working Paper out of print
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.
24
PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE JUNE 1998
88/344: Joerg MAYER Intervention Mechanisms and Symmetry in the EMS
88/345: Keith PILBEAM Exchange Rate Management and the Risk Premium
88/346: Efisio ESPA The Structure and Methodology of International Debt Statistics
88/347: Francese MORATA and and Jaume VERNET
Las Asambleas Régionales en Italia y Espaha: Organizacion Institucional y Réglas de Funcionamiento
88/348: Milica UVALIC The Investment Behaviour of the Labour-Managed Firm: An Econometric Analysis
88/349: Massimo PANEBIANCO Latin-American Identity in the International and Economic Structure
88/350: Gregorio ROBLES La Cour de Justice des CE et les Principes Gânàraux du droit
88/351: Alan KIRMAN On Ants and Markets
88/352: Gianna GIANNELLI Labour Demand, Pricing and Investment Decisions in Italy: An Econometric Analysis
88/353: Niall O'HIGGINS The Progressivity of Government Taxes and Benefits in Ireland: A Comparison of Two Measures of Redistributive Impact
88/354: Christian JOERGES Amerikanische und deutsche Traditionen der soziologischen Jurisprudenz und der Rechtskritk
88/355: Summary of Conference debates and abstracts of selected interventions
The Future Financing Df the EC Budget EPU Conference 16-17 October 1987
:Working Paper out of print
© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.