complexity and the nascent revolution in economics lancaster university dec 9, 2009 w. brian arthur...

Complexity and the Nascent Complexity and the Nascent Revolution in EconomicsRevolution in Economics

Lancaster University

Dec 9, 2009

W. Brian Arthur

External Professor, Santa Fe Institute

© 2009 W. Brian Arthur 2

• Complexity economics, agent-based computational

economics, generative economics, “radical remaking of

economics,” etc.

-- What exactly is going on?

A shift in how we look at the economyA shift in how we look at the economy


What is complexity?What is complexity?

• Elements responding to the pattern their behavior co-creates– A concern with how things form from simpler

elements. – (Usually with system being between order and

chaos)


The economy: naturally complex?The economy: naturally complex?


Standard economics asks: What agent behavior is Standard economics asks: What agent behavior is consistent withconsistent with the pattern it creates? the pattern it creates?– “Solutions” are static equilibria => Equilibrium economics

Complexity economics asks: How does behavior Complexity economics asks: How does behavior adapt adapt

toto the pattern it creates? the pattern it creates?

– Solutions are not necessarily equilibria => Nonequilibrium

economics


Equilibria: Consistency ConditionsEquilibria: Consistency Conditions

• General Equilibrium Theory:General Equilibrium Theory: – What prices and quantities of goods are such that producers

and consumers have no incentive to change behavior?

• Game Theory:Game Theory: – What strategies are mutually consistent?

• Rational Expectations Theory:Rational Expectations Theory: – What forecasts create outcomes that statistically on average

validate those forecasts?


Equilibrium economics: themesEquilibrium economics: themes

• Agents can’t improve on their behavior

– So they must be really smart--hyperrational

– And well informed: problem given and well-

defined for agents

– All information made use of

• Equation based and analytical


Nonequilibrium economics: themesNonequilibrium economics: themes

1. Agents define the problem as they goHence individual cognition becomes important

2. Agents select behaviors in a situation (ecology) their behaviors co-create

Hence such studies are evolutionary

3. Structures “emerge” or are selected probabilisticallyMay be multiple equilibria, one selected

4. Perpetual novelty is possibleBehavior may perpetually cause new structures


The Two Approaches: An ExampleThe Two Approaches: An Example

Q. How do stock markets work? The Asset Pricing Problem


Standard Theory of the Stock MarketStandard Theory of the Stock Market

- Single stock. Random dividend sequence and safe asset

- Investors use an identical forecasting model to buy or sell

Q. What forecasting model would be in equilibrium (upheld on average by the resulting market prices)?

OK. But doesn’t explain real market behavior very well

11 © 2009 W. Brian Arthur

Standard Theory of Asset PricingStandard Theory of Asset Pricing

Forecasting Machine:

E[p(t+1)|I(t)]

MarketMakerBuy/Sell

Orders

InformationI(t)

p(t+1)

Rational Expectations Equilibrium: What forecasting machine is on average validated by {p(t)}?


SFI Artificial Stock MarketSFI Artificial Stock Market(Arthur, Holland, Palmer)(Arthur, Holland, Palmer)

• Artificial “investors” who can form forecasting models or hypotheses about market. They can differ

– Each is an artificially intelligent program

• Otherwise market same as neoclassical

Q. Does standard solution emerge? Or does complex behavior emerge?


Nonequilibrium VersionNonequilibrium Version

Agents must form (possibly different) hypotheses to

forecast

MarketMakerBuy/Sell

Orders

InformationI(t)

p(t+1)

What will be market behavior?

Will this settle to standard outcome?


How our artificially intelligent investors behaveHow our artificially intelligent investors behave

They act inductively:

1. Each has multiple forecasting models or hypotheses

about how the market operates, and uses its currently

most accurate hypothesis

2. They drop poorly performing forecasting models and

generate new ones


Market State Forecast Accuracy

{1100####000: +2.3% 4.2 }{1#00####100: +1.4% 3.6 }{1100####000: -2.1% 1.2 }{1100####000: +0.3% 0.3 }{1000####000: +0.8% 4.5 }{1100####000: -1.2% 4.1 }{0100####000: -5.5% 3.2 }{1100##1#001: +1.1% 2.9 }{11######001: -2.9% 1.3 }{0100####001: +0.4% 1.7 }{0100####010: +1.6% 1.2 }{1100####010: -0.4% 0.2 }

.

.

.

Agent i

A-H-P Architecture: Heterogeneous Agents

Each agent has multiple conditional hypotheses and chooses currently most accurate


Market State Forecast Accuracy

{1100####000: +2.3% 4.2 }{1#00####100: +1.4% 3.6 }{1100####000: -2.1% 1.2 }{1101####000: +0.3% 0.3 }{1000####000: +0.8% 4.5 }{1100##10000: -1.2% 4.1 }{0100####000: -5.5% 3.2 }{1100##1#001: +1.1% 2.9 }{11######001: -2.9% 1.3 }{0100####001: +0.4% 1.7 }{0100####010: +1.6% 1.2 }{1100####010: -0.4% 0.2 }

.

.

.

Agent i

11000010000

Today’s Market State

P(t+1)= 2.3% higher


We find: two regimes for the marketWe find: two regimes for the market

1. If updating (learning) rate is low– Convergence to the standard rational expectations

equilibrium


We find: two regimes for the marketWe find: two regimes for the market

2. If learning rate is higher:

– A market “psychology” emerges

– Technical trading emerges

– Avalanches of change--periods of high and low volatility

– We get Jurassic Park behavior


Complexity economics: Complexity economics: fad or paradigm shift?fad or paradigm shift?

• Sometimes convergence to standard equilibrium outcomes. Equilibrium economics a special case

• Complexity economics is a generalization of standard economics. It is a nonequilibrium economics


Also notice … Also notice …

• What emerges in complexity studies is an “ecology” of behaviours– E.g. an “ecology” of forecasting strategies

• And from time to time this ecology is invaded by new

behaviours or actions


In the real economy,In the real economy,all systems will be gamed …all systems will be gamed …

• Russia’s big bang

• California’s freeing of the electricity market

• Wall Street’s derivatives built on derivatives


Needed: strategic analysis Needed: strategic analysis

of how system could be gamedof how system could be gamed

• Standard, equilibrium economics biases against this– (It wouldn’t be an equilibrium if someone could take

advantage of it)

• Nonequilibrium economics asks

– What new strategies can gain a hold?


EEEqqquuuiiillliiibbbrrriiiuuummm EEEcccooonnnooommmiiicccsss NNNooonnneeeqqquuuiiillliiibbbrrriiiuuummm EEEcccooonnnooommmiiicccsss

Elements consistent with… Elements react to …

Metaphor: machine Metaphor: an ecology

Simplified assumptions(e.g. homogeneous agents)

More realistic assumptions(e.g. heterogeneous agents)

Hyperrational behavior Cognitive behavior

Static equilibrium

Market outcome optimal

Evolving pattern, perpetual novelty

The system can be gamed

complexity and the nascent revolution in economics lancaster university dec 9, 2009 w. brian arthur...

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