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) (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.”

- Microscopic Investors and Macroscopic Crashes MICRO - Investors, individual capital,shares INTER - sell/buy orders, gain/loss MACRO - social wealth distribution, market price fluctuations (cycles, crashes, booms, stabilization by noise) “ Levy, Solomon and Levy's Microscopic Simulation of Financial Markets points us towards the future of financial economics. If we restrict ourselves to models which can be solved analytically, we will be modeling for our mutual entertainment, not to maximize explanatory or predictive power." HARRY M. MARKOWITZ, Nobel Laureate in Economics

Stock market shock explained Physicists model recent trading frenzy. Market 'spikes' are seen by traders as freak events. Physicists expect them

Simplest model: A opportunities ; B capital 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 a -  <0 #b#b a  b. = ( a -  )  b + D b  b –  b 2 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 << 0 ! Multi-Agent Complex Systems Implications: one can prove rigorously that the DE prediction: Time Differential Eqations ( continuum << 0 approx ) Multi-Agent stochastic  a   prediction Is ALWAYS wrong !

and Branching Random Walks Theorems (2002) that : - In all dimensions d:  D a > 1-P d always suffices P d = Polya ’ s constant ; P 2 = 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 Surface one can prove rigorously by RG

Polish Economy after Liberalization Data Andrzej Nowak (+group) Kamil Rakocy Gur Ya’ari, SS(+group)

EXAMPLE of Theory Application APPLICATION: Liberalization Experiment Poland Economy after MICRO growth ___________________ => MACRO growth 1990 MACRO decay (90) 1992 MACRO growth (92) 1991 MICRO growth (91) GNP 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.), CO 3 collaboration

GNP Complexity prediction Maps Andrzej Nowak ’ s group (Warsaw U.), CO 3 collaboration

MOVIE

No correlation in economic activity No correlation in growth No correlation of economic activity or of growth rate to education Communist regime Educated center Frontier of Poland Economic activity

First year of liberalization Decay in global economic activity Singular points of development (growth in activity) No spatial correlation in activity But some short range correlation in growth rate Growth rate short correlated to education

Second-Third year of liberalization Still some decay but regions of growth expand So space correlation in growth rate but not clear correlation to distance in activity itself Correlation of growth to education (but less of activity itself)

Number of enterprizes per capita We can actually see the forming of a spatially correlated structure of this parameter

Forth and further years The diffusion insures that the growth rate is now uniform so no spatially correlated and not correlated to education.. The activity itself is correlated to education and spatially correlated around it.

MOVIE

alpha only during the first 4-5 years we observe these Correlations