Transcript w MAX - Sorin Solomon

Complexity Emergence in Economics
Sorin Solomon,
Racah Institute of Physics HUJ Israel
Scientific Director of Complex Multi-Agent Systems Division, ISI Turin
and of the Lagrange Interdisciplinary Laboratory for Excellence In Complexity
Coordinator of EU General Integration Action in Complexity Science
Chair of the EU Expert Committee for Complexity Science
MORE IS DIFFERENT (Anderson 72; Nobel for Physics 77)
(more is more than more)
Complex “Macroscopic” properties may be the
collective effect of
many simple “microscopic” components
Phil Anderson “Real world is controlled …
– by the exceptional, not the mean;
– by the catastrophe, not the steady drip;
– by the very rich, not the ‘middle class’.
we need to free ourselves from ‘average’ thinking.”
“MORE IS DIFFERENT”
Complex Systems Paradigm
MICRO - the relevant elementary agents
Traders, investors
INTER
transactions
- their basic, simple interactions
MACRO - the emerging collective objects
herds,crashes,booms
Intrinsically (3x) interdisciplinary:
-MICRO belongs to one science Decision making, psychology
-MACRO to another science
-Mechanisms: a third science
economics
statistical mechanics, physics
math, game theory, info
“Levy, Solomon and Levy's
Microscopic
Simulation of
Financial Markets
points us towards
the future of financial
economics”
HARRY M. MARKOWITZ,
Nobel Laureate
in Economics
1990
4100
4050
4000
3950
3900
3850
3800
3750
9
9.5
10
10.5
11
11.5
Suppose you are the president of a region, or
the president of its industrialists association
The new statistics are in:
the economy is decaying by 10%.
Is it good news or bad news?
On top of it , some of the major enterprises
(representing 50% of the economy)
are decaying by 40%.
Is it good news or bad news?
If the average growth rate is -10% and
the major enterprises
(50% of the economy) are going down by -40%,
it means that there are enterprises
in the other 50% that are growing by + 20%.
If you let them develop,
in 4 years: they will grow by (1.20)4 = double !
(they alone will equal the volume of the total initial
economy).
From that moment on, the
region economy will have a total growth rate of ~ 20%
What would be the worse thing to do?
To try to insure a uniform rate of growth
by differential taxation and subsidies:
Put together the -40% of the losers,
with the +20% of the successful and
get together a uniform NEGATIVE growth rate
-10%: everybody collapses!
These scenarios look
oversimplified, unrealistic and unpractical
but actually this is somewhat
what happened [in both directions]
in quite a number of countries around the 1990’s.
I present in the sequel
data and theoretical study of
Poland's 3000 counties over 15 years
following the 1990 liberalization of the economy.
The data tells a very detailed story similar to the
above but a little bit more sophisticated.
To understand it we have to
go back in time more then
200 years ago in Holland.
(but don't worry, we will soon get back toTorino
(Pareto, Volterra) to get more info).
Malthus : autocatalitic proliferation/ returns :B+AB+B+A
BØ
death/ consumption
dw/dt = a w
a =(#A x birth rate a =(#A x returns rate -
death rate)
consumption /losses rate)
exponential solution: w(t) = w(0)e a t
w=
#B
birth rate > death rate
a>0
birth rate > death rate
a<0
TIME
Verhulst way out of it: B+B B
The LOGISTIC EQUATION
dw/dt = a w – c w2
c=competition / saturation
Solution: exponential ==========saturation at X= a / c
w = #B
almost all the social phenomena, except in their
relatively brief abnormal times obey the logistic growth.
“Social dynamics and quantifying of social forces”
Elliott W. Montroll
US National Academy of Sciences and
American Academy of Arts and Sciences
'I would urge that people be introduced to the
logistic equation early in their education…
Not only in research but also in the everyday
world of politics and economics …”
Nature
Robert McCredie,
Lord May of Oxford,
President of the Royal Society
Reality
Discrete Individuals
SAME
SYSTEM
Models
Continuum Density
Complex ----------------------------------Trivial
Localized patches -----------------------Spatial Uniformity
Adaptive ----------------------------------Fixed dynamical law
Development -----------------------------Decay
Survival -----------------------------------Death
Misfit was always assigned to the neglect of specific details.
We show it was rather due to the neglect of the discreteness.
Once taken in account => complex adaptive collective objects.
emerge even in the worse conditions
Logistic Equation usually ignored spatial distribution,
Introduce discreteness and randomeness !
.
w =
( conditions x birth rate - death) x w + diffusion w
- competition w2
conditions is a function of
many spatio-temporal
distributed discrete
individual contributions
rather then totally uniform
and static
Phil Anderson
“Real world is controlled …
– by the exceptional, not the mean;
– by the catastrophe, not the steady drip;
– by the very rich, not the ‘middle class’
we need to free ourselves
from ‘average’ thinking.”
Shnerb, Louzoun, Bettelheim, Solomon,[PNAS (2000)] proved by (FT,RG)
that the continuum , differential logistic equation prediction:
Multi-Agent <a> <<
prediction
0
Differential Eqations
a << 0 approx)
(continuum
Time< >
Is ALWAYS wrong !
Instead: emergence of singular
spatio-temporal localized
collective islands with
adaptive self-serving behavior
=> resilience and sustainability
even for <a> << 0!
Electronic Journal of Probability
Vol. 8 (2003) Paper no. 5, pages 1–51.
Branching Random Walk with Catalysts
Harry Kesten, Vladas Sidoravicius
Shnerb et al. (2000), (2001) studied the following system of interacting particles on Zd:
There are two kinds of particles, called A-particles and B-particles. The A-particles
perform continuous time simple random walks, independently of each other. The
jumprate of each A-particle is DA. The B-particles perform continuous time simple
random walks with jumprate DB, but in addition they die at rate and a B-particle at x at
time s splits into two particles at x during the next ds time units with a probability NA(x,
s)ds+o(ds), where NA(x, s) (NB(x, s)) denotes the number of A-particles (respectively
B-particles) at x at time s. Conditionally on the A-system, the jumps, deaths and
splittings of different B-particles are independent. Thus the B-particles perform a
branching random walk, but with a birth rate of new particles which is proportional to
the number of A-particles which coincide with the appropriate B-particles. One starts
the process with all the NA(x, 0), x 2 Zd, as independent Poisson variables with mean
μA, and the NB(x, 0), x 2 Zd, independent of the A-system, translation invariant and
with mean μB. Shnerb et al. (2000) made the interesting discovery that in dimension 1
and 2 the expectation E{NB(x, t)} tends to infinity, no matter what the values of , ,DA,
DB, μA, μB 2 (0,1) are.
We have only changed the notation slightly and made
more explicit assumptions on the initial distributions than Shnerb et al. (2000). Shnerb et
al. (2000) indicates
that in dimension 1 or 2 the B-particles “survive” for all choices of the parameters ,
,DA,DB, μA, μB > 0.
However, they deal with some form of continuum limit of the system and we found it
difficult to interpret
what their claim means for the system described in the abstract. For the purpose of this
paper we shall say
that the B-particles survive if
lim sup
t!1
P{NB(0, t) > 0} > 0, (1.1)
where P is the annealed probability law, i.e., the law governing the combined system of
both types of particles.
We shall see that in all dimensions there are choices of , ,DA,DB, μA, μB > 0 for which
the B-particles
do not survive in the sense of (1.1). A much weaker sense of survival is that
lim sup
t!1
ENB(0, t) > 0. (1.2)
Our first theorem confirms the discovery of Shnerb et al. (2000) that even more than
(1.2) holds in dimension
1 or 2 for all positive parameter values. Note that E denotes expectation with respect to
P, so that this
Movie By Gur Ya’ari
.
2
w =aw–cw
Logistic Diff Eq prediction:
Multi-Agent stochastic
<a> << 0
prediction
Differential Equations continuum
<a> <<Time0 approx)
GDP
Poland
Nowak, Rakoci, Solomon, Ya’ari
The GDP rate of Poland, Russia and Ukraine
(the 1990 levels equals 100 percent)
Poland
Russia
Ukraine
Belarus
Year
% change
1997
3.1
1998
4.1
1999
1.3
2000
2.2
2001
3.3
2002
4.4
2003
4.0
Slovakia
Kazahstan
Hungary
Nowak, Rakoci, Solomon, Ya’ari
Nowak, Rakoci, Solomon, Ya’ari
One may represent the dynamics of the counties economies by
the following system of coupled differential equations
d wi / dt = (ai -∑ j rji )wi + ∑j rij wj – ∑j wi cik wk
d wi / dt = the growth rate of county i
aiwi =endogenous proliferation rate in county i
∑j rij wj = the growth due to transfer from other
counties
-
∑ j rji wi =the capital transfer to other counties
∑j wi cik wk = the competition and other
interaction factors with other counties and the
environment
Predicted Scenario:
First the singular educated centers WMAX develop
while the others WSLOW decay
d wMAX / dt
~ (aMAX - ∑ j rj ;MAX )wMAX >>0
d wSLOW / dt ~ (aSLOW -∑ j rjSLOW )wSLOW <<0
Then, as WMAX >> WSLOW , the transfer becomes
relevant and activity spreads from MAX to SLOW and
all develop with the same rate aMAX -∑ j rji but
preserve large inequality
d wSLOW / dt ~ rSLOW, MAX wMAX
=>wSLOW/wMAX ~ rSLOW MAX / (aMAX-ai)
These predictions are confirmed strongly by the data
Nowak, Rakoci, Solomon, Ya’ari
d wi / dt = (ai -∑ j rji )wi + ∑j rij wj – ∑j wi cik wk
Couthy Growth= Local Proliferation + transfer from others + saturation
• Case 1: low level of capital redistribution
rj , MAX << (aMAX – aj )
-high income inequality wi/wMAX ~ riMAX/(aMAX-ai)
-outbreaks of instability (e.g. Russia, Ukraine).
•Case2: high level of central capital redistribution
(as in the previous, socialist regime)
rj , MAX >> (aMAX – aj )
- slow growth or even regressing economy (Latvia) but quite
- uniform wealth in space and time.
•Case 3 :Poland seems - optimal balance :
aj , MAX are large enough to insure adaptability and sustainability
over a large number of counties yet the
aMAX - ∑ j rjMAX is still large enough to insure overall growth.
Romania
Poland
Russia
Latvia
Ukraine
Instability of over-localized
civilizations
Very few localized growth centers
(occasionally efficient but unequal and unstable)
Intermediate Range
Uniform distribution (unefficient but stable (decay))
Prediction
the economic inequality (Pareto exponent)
and
the economic instability
(index anomalous fluctuations exponent)
It is also strongly confirmed
(the data we had were from western economies)
a
400
Forbes 400 richest by rank
b
What next?
Measure Changes
in ai due to Fiat
plant closure
PIEMONTE MAP
With Prof Terna’s
group
Check
alternatives