Complexity Emergence in EconomicsSorin 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)(more is more than more)Complex “Macroscopic” properties may be the collective effect of simple interactions betweenmany elementary “microscopic” components

MICRO - Investors, individual capital ,shares         INTER - sell/buy orders, gain/loss          MACRO - social wealth distribution, market price fluctuations (cycles, crashes, booms, stabilization by noise)

HARRY M. MARKOWITZ, Nobel Laureate in Economics

“Levy, Solomon and Levy's

Microscopic Simulation of

Financial Markets points us towards

the future of financial economics”

9 9.5 10 10.5 11 11.53750

3800

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Stock market shock explainedPhysicists model recent trading frenzy.

Market 'spikes' are seen by traders as freak events.Physicists expect them

• A+B-> A+B+B proliferation

• B-> . death

• B+B-> B competition (radius R)

almost all the social phenomena, …. obey the logistic growth. “Social dynamics and quantifying of social forces” E. W. Montroll 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 … Lord Robert May

b.

= ( a -)b – b 2 (assume 0

dim!!!)

Simplest Model: A= gain opportunities, B = capital

WELL KNOWN Logistic Equation (Malthus, Verhulst, Lotka, Volterra, Eigen)

Instead: emergence of singular spatio-temporal localized collective islands with adaptive self-serving behavior

=> resilience and sustainability

even for < a-> << 0!

Diff Eq prediction:

Time

Differential Equations continuum

a << 0 approx)

Multi-Agent stochastic

a

prediction

One Proved Rigorously that DE is ALWAYS wrong in dim >0 !

b.

= ( a -)b – b 2

and Branching Random Walk Theorems (2002) that:

- In all dimensions d: Da > 1-Pd

always suffices

Pd = Polya’s constant ; P2 = 1

-On a large enough 2 dimensional surface, the B population always grows!No matter how fast the death rate ,

how low the A density, how small the

proliferation rate

The Importance of Being Discrete; Life Always Wins on the Surfaceone can prove rigorously by RG

Discrete A Individuals microscopic noiseAutocatalytic B proliferation amplification

Collective Macroscopic Objects

-Power Laws: - wealth distribution-

- Levy, fractal, market fluctuations-

-Emergent Properties : Adaptability

- Most singular , rarest fluctuations dominate the system dynamics

The Importance of Being Discrete; Life Always Wins on the Surface

= !!!

Polish Economy after LiberalizationData

• Andrzej Nowak (+group)

• Kamil Rakocy

• Gur Ya’ari, SS(+group)

EXAMPLE of Theory Application

APPLICATION: Liberalization Experiment Poland Economy after 1989

+ MICRO growth___________________

=> MACRO growth

1990 MACRO decay (90)

1992 MACRO growth (92)

1991 MICRO growth (91)

GNP

89 90 91 92

THEOREM (RG, RW) one of the fundamental laws of complexity

Global analysis prediction

Complexity prediction

Education 88

MACRO decay

Maps Andrzej Nowak’s group (Warsaw U.), CO3 collaboration

GNP

89 90 91 92

Complexity prediction

Maps Andrzej Nowak’s group (Warsaw U.), CO3 collaboration

pclin_rot.mpeg

MOVIE

Spatial Correlation of Number of enterprizes per capita

One can see the forming of a spatially correlated patches

The risk of being unfair, the unstable fate of globalization. Louzoun. Y. Mazurski. D., Goldberg. J. Solomon. S. Artificial Life 4(9) 357 (2003)

Growth Rate Spatial CorrelationsSignificant only during first 4-5 years

THEN:

uniform country

growth rate

(by diffusion)

[THEOREM]Co-Evolutionist Stochastic Dynamics: Emergence of Power-Laws in stochastic Lotka-Volterra-Eigen-Schuster Systems S. Solomon, P. Richmond, O. Biham and O. Malcai, (2003)

Further Rigorous Theoretical Results: Even in non-stationary, arbitrarily varying conditions (corresponding to wars, revolutions, booms, crashes, draughts)

Indeed it is verified:

the list of systems presenting scalingfits empirically well

the list of systems

modeled in the past by logistic equations !

that stable Power Laws

emerge generically from

stochastic logistic systems

The Theorem predicts:

Stable power laws in variable economies; Lotka-Volterra implies Pareto-Zipf S. Solomon and P. Richmond Eur. Phys. J. B 27, 257-261 (2002)

VERY NON TRIVIAL PREDICTION Relating

Market Index Dynamicsto

Individual Wealth Distribution:

Dell

Buffet

20ALLEN

GATES

WALMART

1/

NOT disputed by Yakovenko etc

Individual Wealth Distribution

Pareto-ZIPF law

Mantegna and Stanley The distribution of stock index variations for various values of

the time interval

The probability

of the price being the same afteras a function of the time interval :

P(0,–

Market Index Dynamics

NOT disputed by the faster then Levy tail decay analysis !

Stock Index Stability in time

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Dell

Buffet

20ALLEN

GATES

WALMART

Stock Index Stability in time

Time Interval (s)

P

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of

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Rank in Forbes 400 list

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Theoretical Prediction

Forbes 400 richest by rank

400

Confirmed brilliantlyPioneers on a new continent: on physics and economics Sorin Solomon and Moshe Levy Quantitative Finance 3, No 1, C12 2003