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Complexity and Economics

The lowest simplicity you can achieve is the complexity Jo˜ ao Basilio Pereima joaobasilio@ufpr.br

Department of Economics Graduate Program in Economic Development Curitiba-Paran´ a-Brazil

6 de marc ¸o de 2015

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Complexity and Economics CLASS 01

Complexity in General Science

Complexity and Economics 6 de marc ¸o de 2015 2 / 25

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Oppening

Economics and Complexity is an introductory course for researchers and graduated students of economy who wish to comprehend the complex approach applied in economics and learn how to build agent based models. The curse aims to introduce

• ntological concepts and definitions, set out examples of what is a complex system and

how these systems works and evolve in time. In a more pragmatic way the course aims to introduce two specific tools used to build up economic agent based models: the Laboratory of Simulation and Development (LSD) and Netlogo. Some economic and social models will be built by using computational resources intensively . Massive attention will be spent in theoretical questions in economics and programming methods and activities applied in developing agent-based models (ABM).

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Complexity - Motivations (Science with a pinch of emotion)

I think the next century will be the century of complexity.

Stephen Hawking - January 2000

Complexity and Economics 6 de marc ¸o de 2015 4 / 25

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Complexity - Motivations (Science with a pinch of emotion)

Science has explored the microcosmos and the macrocosmos; we have a good sense of the lay of the land. The great unexplored frontier is complexity

Heinz-Pagels: The Dreams of Reason

Complexity and Economics 6 de marc ¸o de 2015 5 / 25

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Complexity - Motivations (Science with a pinch of emotion)

Science has explored the microcosmos and the macrocosmos; we have a good sense of the lay of the land. The great unexplored frontier is complexity

Heinz-Pagels: The Dreams of Reason

Economic science has explored the microeconomics and the macroeconomics; we have a (not so) good sense of the economic system. The great unexplored frontier is complexity

Basilio, this economic course

Complexity and Economics 6 de marc ¸o de 2015 5 / 25

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Why economists do not understand Complexity well, if so? Our brains were designed to understand hunting and gathering, mating and child-rearing: a world of medium-sized objects moving in three dimensions at moderate speeds.

Dawkins (1987) in The Blind Watchmaker

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Frozen view?

“Economic is not a evolutionary science - by the confession of its spokesman: and the economists turn their eyes with something of envy and some sense of baffled emulation to theses rivals that make broad their phylacteries [phylum] with the legend, ‘Up to date’. Precisely wherein the social and political sciences, including economics, fall short of being evolutionary sciences, is not so plain. ”

Complexity and Economics 6 de marc ¸o de 2015 7 / 25

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Frozen view?

“Economic is not a evolutionary science - by the confession of its spokesman: and the economists turn their eyes with something of envy and some sense of baffled emulation to theses rivals that make broad their phylacteries [phylum] with the legend, ‘Up to date’. Precisely wherein the social and political sciences, including economics, fall short of being evolutionary sciences, is not so plain. ”

Veblen (1899, p. 374-5)

The same reasoning applies today to the Complexity Theory context. Ex.: Arthur (1994, 1999)

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Reductionism and Complexity

Reductionism is the most natural thing in the world to grasp. It’s simply the belief that “a whole can de understood completely if you understand its parts, and the nature of their ‘sum’ ”. No

• ne in her left brain could reject reductionism.

Hofstadter (1979, p. 318)

The scientif method: “To dive all the difficulties under examination into as many parts as possible, and as many as were required to solve then” and “to conduct my thoughts in a give

• rder, beggining with the simplest and most easily understood objects, and gradually ascending,

as it were step by step, to the knowledge of the most complex”

Descartes (1637)

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Why Complexity

• Many phenomena in the physic, natural and social dimension of the reality can not

be explained with concepts of mechanical physic

• Large structures are assembled from particles or individuals in a way far beyond

that the simple aggregation and sum

• Structures evolves to an unpredictable future and forms
• The time arrow is not reversible and many traditional scientific methods fails to

explain and forecast

• Commonly the systems shows up heterogeneity and produces novelty
• The system (societies) are populated by ± heterogeneous agent who interacts

with the others

• We are far from comprehend the World or the Reality with the newtonian machine
• r statistical viewpoint, mainly in social and economic science
• Statistical versus Deterministic versus Complexity view of the world

Complexity and Economics 6 de marc ¸o de 2015 9 / 25

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Why Complexity

• Many phenomena in the physic, natural and social dimension of the reality can not

be explained with concepts of mechanical physic

• Large structures are assembled from particles or individuals in a way far beyond

that the simple aggregation and sum

• Structures evolves to an unpredictable future and forms
• The time arrow is not reversible and many traditional scientific methods fails to

explain and forecast

• Commonly the systems shows up heterogeneity and produces novelty
• The system (societies) are populated by ± heterogeneous agent who interacts

with the others

• We are far from comprehend the World or the Reality with the newtonian machine
• r statistical viewpoint, mainly in social and economic science
• Statistical versus Deterministic versus Complexity view of the world

Despite the progress of science in the XX century, many questions and answers remains open and can not be thought with traditional viewpoint

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So, what is complexity?

An interdisciplinary field of research that seeks to explain how large number of relatively simple entities

• rganize themselves, without the benefit of any central controller into a collective whole that creates

patterns, uses information, and, in some cases, evolves and learns.

Mitchell (2009, p.4)

Complexity and Economics 6 de marc ¸o de 2015 10 / 25

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So, what is complexity?

An interdisciplinary field of research that seeks to explain how large number of relatively simple entities

• rganize themselves, without the benefit of any central controller into a collective whole that creates

patterns, uses information, and, in some cases, evolves and learns.

Mitchell (2009, p.4)

Complex systems consist of units interacting in a hierarchy of levels, including subsystems composed of even more intricate sub-subsystems. Complex systems exhibit emergent properties due to the interaction of their subsystems when certain unspecific environmental conditions are met, and they show temporal and/or spatial patterns on a scale that is orders of magnitude bigger than the scale on which the subsystems interact.

Fuchs (2013, p.4)

A complex thing is something whose constituent parts are arranged in a way that is unlikely to have arisen by chance alone.

Dawkins (1987, p.7)

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So, what is complexity?

A system of connected agents that exhibits an emergent global behavior not imposed by a central controller, but resulting from the interactions between agents.

Boccara (2004, p.4)

The science of complexity suggests that while life is in accordance with the laws of physics, physics cannot predict life.

´ Erdi (2008, p.5)

Complexity results from the inter-relationship, inter-action and inter-connectivity of elements within a system and between a system and its environment. Murray Gell-Mann, in Complexity Vol. 1, No. 5, 1995/96, traces the meaning of complexity to the root of the word. Plexus means braided or entwined, from which is derived complexus meaning braided together, and the English word complex is derived from the

• Latin. Complexity is therefore associated with the intricate inter-twining or inter-connectivity of elements

within a system and between a system and its environment.

Chan (1997)

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Ants, Neurons, Crowd and other complex system

Complexity and Economics 6 de marc ¸o de 2015 12 / 25

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Ants, Neurons, Crowd and other complex system

Complexity and Economics 6 de marc ¸o de 2015 12 / 25

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Ants, Neurons, Crowd and other complex system

Complexity and Economics 6 de marc ¸o de 2015 12 / 25

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Ants, Neurons, Crowd and other complex system

Complexity and Economics 6 de marc ¸o de 2015 12 / 25

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Complexity Approaches

Important concepts

• Diversity/variety
• High Non-linearity
• Hierarchy
• Non-Predictability
• Interactions (at micro and macro

level)

• Network
• Self organization
• Adaptative system
• Emergence
• Learning and information

computation

• Evolution

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Complexity Approaches

• Non-linear system of differential equations (at macro level)
• Instability
• Multiple equilibrium
• Dynamic replicator or Lotka-Voltera system
• Bifurcation
• Deterministic Chaos
• Fractal structures

Complexity and Economics 6 de marc ¸o de 2015 14 / 25

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Complexity Approaches

• Non-linear system of differential equations (at macro level)
• Instability
• Multiple equilibrium
• Dynamic replicator or Lotka-Voltera system
• Bifurcation
• Deterministic Chaos
• Fractal structures
• Agent-based models with interactions
• Genetic Algorithms/Evolutionary Computation
• Cellular Automata
• Networks
• Spatially Oriented models (e.g. using Netlogo)
• Micro-macro models in difference (e.g. using LSD in economic models)

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Complexity Approaches

• Non-linear system of differential equations (at macro level)
• Instability
• Multiple equilibrium
• Dynamic replicator or Lotka-Voltera system
• Bifurcation
• Deterministic Chaos
• Fractal structures
• Agent-based models with interactions
• Genetic Algorithms/Evolutionary Computation
• Cellular Automata
• Networks
• Spatially Oriented models (e.g. using Netlogo)
• Micro-macro models in difference (e.g. using LSD in economic models)
• Evolution, Adaptive System and Computation
• Computation of information
• Individual change
• Structural change
• Path-dependence and cumulative causation (Myrdal)
• Auto-organization (from chaos to order)

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Non-linear system of differential equation

Figura : Thomas Malthus - 1766-1839

The malthusian exponenctial equation is (Malthus, 1798)

dN(t) dt = rN(t) − → N(t) = N(0)ert It is a one dimensional equation

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Non-linear system of 1 differential equation

Figura : Pierre Franc ¸ois Verhulst - 1804-1849

The logistic equation was coined by Verhulst (1838)

dN(t) dt = rN(t)

• 1 − N(t)

K

• −

→ N(t) = K 1 + CKe−rt where C =

1 N(0) − 1 K

is the constant of integration and initial condition. It is a one dimensional quadratic equation and K is the carry capacity.

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Non-linear system of 1 differential equation

Logistic function: from linear behavior to deterministic chaos

dN(t) dt = rN(t)

• 1 − N(t)

K

• Complexity and Economics

6 de marc ¸o de 2015 17 / 25

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Non-linear system of 2 differential equation

The van der Pol (1926) model

˙ x(t) = y(t) ˙ y(t) = α

• 1 − x(t)2

y(t) − x(t) Phase Diagram

View it in Maple...

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Non-linear system of 3 differential equation

The Lorenz (1963) Attractor model

˙ x(t) = σ (y(t) − x(t)) ˙ y(t) = x(t) (−ρ − z(t)) − y(t) ˙ z(t) = −βz(t) + x(t)y(t)

Mostrar modelo no Maple... and on the Wikipedia:

http://en.wikipedia.org/wiki/Lorenz_system

Complexity and Economics 6 de marc ¸o de 2015 19 / 25

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The World of Interacting Agents

All the preceding examples were based in evolution of agregated, summed up or average quantities. No heteregeneity or interactions was present. In the Agent-based-world, the behavior of an agents have an effect on the others, and individual following a simple and particular rule, can produce surprising aggregated

• effects. Stem cell can divide yourself and generate diferent organs. One initial cell

generate a complete and different body within the same species. Individuals following his particular or collective simple rule generate a social or economic reality, observed and analysed by the traditional methodos: econometrics and structural models. The aggregated researcher can not answer suitably the question: Where does this aggregated pattern cames from? In order to answer this you need a agent-based-world (model) inhabited by heterogeneous agents more than representative one.

Complexity and Economics 6 de marc ¸o de 2015 20 / 25

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Cellular Automata-CA

At a very general level, one might say that computation is what a complex system does with information in order to succeed or adapt in its enviromnet. Mitchell (2009, cap. 10,

• p. 146)

The CA is a kind of complex system where the agents (cell) can change its status or move to another place according to a set of disposal simple rule and depending of the status of its neighborhood. The CA generaly is represented in a Lattice (grid) of cells.

Game of Life (Conway) and Wolfram Cellular Automata

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Information, computation and some amazing numbers

Evolution has been processed by computation. How the evolution process manipulates the information? Dawkins (1987): by a Blinded Watchmaker. Evolution goes on by small and located random mutation towards a long and slow and cumulative selection. Consider a system composed by “n” constituents (agents) or a space-state with “n” configuration who or which presents only two characteristics or attribute a = {0, 1} which can means black and white, optimistic and pessimistic, altruist or selfish, or anything else. If we arrange this “n” components in a one-dimensional sequence we get an array or a landscape with many different results or configuration at instant t:

N=2 N=3 A={0, 0}, {0, 1}, {1, 0}, {1, 1} A={0, 0, 0}, {0, 0, 1}, . . . , {1, 1, 1} A = 22 = 4 A = 23 = 8 N=100 A = 2100 = 1.267.650.600.228.229.401.496.703.205.376 = 1, 267E30

Complexity and Economics 6 de marc ¸o de 2015 22 / 25

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Information, computation and some amazing numbers

Evolution has been processed by computation. How the evolution process manipulates the information? Dawkins (1987): by a Blinded Watchmaker. Evolution goes on by small and located random mutation towards a long and slow and cumulative selection. Consider a system composed by “n” constituents (agents) or a space-state with “n” configuration who or which presents only two characteristics or attribute a = {0, 1} which can means black and white, optimistic and pessimistic, altruist or selfish, or anything else. If we arrange this “n” components in a one-dimensional sequence we get an array or a landscape with many different results or configuration at instant t:

N=2 N=3 A={0, 0}, {0, 1}, {1, 0}, {1, 1} A={0, 0, 0}, {0, 0, 1}, . . . , {1, 1, 1} A = 22 = 4 A = 23 = 8 N=100 A = 2100 = 1.267.650.600.228.229.401.496.703.205.376 = 1, 267E30 The size of Universe: 1.2 to 3.0E1023 stars → 1078 to 1082 atoms

Complexity and Economics 6 de marc ¸o de 2015 22 / 25

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Agent-Based Models

Exemplos no Netlogo

• 1. Computer Science/Cellular Automata/Life (Game of Life)
• 2. Social Science/El Farol
• 3. Social Science/SugarSpace3
• 4. Sbicca & Pereima (2014)

Exemplos no LSD

• 1. Brian Arthur
• 2. Nelson & Winter
• 3. Higachi & Pereima (2015)

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Complexity and Economics CLASS 02

Complexity in Economic Science

(Under construction)

Complexity and Economics 6 de marc ¸o de 2015 24 / 25

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Referˆ encias I

Arthur, W. B. (1994). Inductive reasoning and bounded rationality. The American Economic Review, 84(2):406–411. Papers and Proceedings of the Hundred and Sixth Annual Meeting of the American Economic Association (May). Arthur, W. B. (1999). Complexity and the economy. Science, 284(5411):107–109. 2 april 1999. Boccara, N. (2004). Modeling Complex Systems. Springer Verlag New York Inc, USA. Chan, S. (1997). Complex adaptative systems. Mimeo. ESD.83 Research Seminar in Engineering Systems. Dawkins, R. (1987). The Blind Watchmaker: Why the evidence of evolution reveals a universe without

• design. W. W. Norton & Company Inc., New York, USA. Reprinted edition 1996.

Descartes, R. (1637). Discourse on the method. Oxford University Press, London. Oxford World’s Classic, printed in 2006. ´ Erdi, P. (2008). Complexity Explained. Springer-Verlag, Berlin Heidelberg. Fuchs, A. (2013). Nonlinear Dynamics in Complex System: Theory and Appliations for the Life, Neuro, and Natural Sciences. Springer-Verlag, Berlin. Hofstadter, D. R. (1979). G¨

• del, Escher, Bach: an Eternal Golden Braid. Basic Book, New York.

Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2):130–141. Malthus, T. (1798). An Essay on the Principle of Population. John Murray, London, 6th edition. 1826. Mitchell, M. (2009). Complexity: a Guide Tour. Oxford University Press, Oxford, USA. van der Pol, B. (1926). On relaxation-oscillations. Philosophical Magazine and Journal of Science, 2(7). Veblen, T. (1899). A Teoria da Classe Ociosa: Um Estudo Estudo Economico das Instituic ¸˜

• es. Abril

Cultural, colec ¸˜ ao Os Economistas, Trad. portuguˆ es 1983, S˜ ao Paulo. Verhulst, P. F. (1838). Notice sur la loi que la population poursuit dans son accroissemen. Correspondance math´ ematique et physique, 10:113–121.

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