Complexity in the Economy and Business IBM Almaden Institute April 12, 2007 W. Brian Arthur External Professor, Santa Fe Institute

Complexity in the Complexity in the Economy and BusinessEconomy and Business

IBM Almaden Institute

April 12, 2007

W. Brian Arthur

External Professor, Santa Fe Institute

© 2007 W. Brian Arthur 2

• Complexity economics, agent-based computational

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


The economy is naturally complexThe economy is 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

– General equilibrium theory

– Game theory

– Rational expectations economics


Complexity economics asks: How does Complexity economics asks: How does behavior behavior adapt toadapt to the pattern it creates? the pattern it creates?

• Solutions not necessarily in equilibrium

• Therefore a non-equilibrium economics


Standard economicsStandard economics

• Need to model rationality of agents

– Identical agents who use perfect rationality

– Problem given and well-defined for agents

– Equation based


Non-equilibrium economicsNon-equilibrium economics

• Need to model process of adjustment for agents

– Possible perpetual novelty

– “Cognitive agents” who may differ

– Evolutionary setup natural

– Algorithmic


Standard economics based on diminishing Standard economics based on diminishing returns (negative feedbacks)returns (negative feedbacks)

• Keeps equilibrium unique


Increasing Increasing returnsreturns problems problems difficult to deal withdifficult to deal with

Example:

N firms (or technologies, or regions) compete, and as one gets ahead it gains further advantage

• What is the outcome? – Static approach doesn’t work


Dealing with increasing returnsDealing with increasing returns

Redefine the problem as a stochastic process

• Solution properties: – Multiple possible outcomes– Not predictable which outcome– History dependent– Outcome locked in– Outcome asymmetric


The Two Approaches: An ExampleThe Two Approaches: An Example SFI Artificial Stock MarketSFI Artificial Stock Market

Arthur, Holland, LeBaron, Palmer, Tayler (1997)Arthur, Holland, LeBaron, Palmer, Tayler (1997)

• How do stock markets work? – The Asset Pricing Problem

13 © 2007 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)}?


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:

– Each has multiple forecasting models or hypotheses

about how the market operates

– Each uses its currently most accurate hypotheses

– They drop poorly performing forecasting models and

generate new ones


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

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

• This is a generalization of standard economics


Implications for policyImplications for policy

• Standard economics: Get conditions right, don’t intervene

• Nonequilibrium economics: Multiple possible outcomes. A nudging hand.

Become aware of adjustment problems– E.g. Russia’s big bang


How does this apply in business?How does this apply in business?

• Seeing business from an ecological viewpoint

• Awareness of defining problem as you go


How does this apply in business?How does this apply in business?

• Planning. But allowing some structures to “emerge”

• Providing “libraries” of solutions


OOOlllddd EEEcccooonnnooommmiiicccsss NNNeeewww EEEcccooonnnooommmiiicccsss

Equilibrium economics(elements consistent with…)

Nonequilibrium economics(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 Evolving pattern, perpetual novelty



Example: the El Farol problemExample: the El Farol problem

One hundred people must decide independently each week whether to show up at their favorite bar.

– Rule: if a person predicts that more than 60 will attend, he will avoid the crowds and stay home

– if he predicts fewer than 60 he will go

Q. How do you predict attendance? – Rational expectations fails


El FarolEl Farol--how agents learn--how agents learn

• The bar-goers form hypotheses about the problem and act on currently most accurate of these

• Ann “ecology” of beliefs emerges. “ecology” of beliefs emerges. Changes over timeChanges over time

I.e. a “psychology” of the market emerges


• Standard economics: what behavior is consistent consistent

withwith the pattern it creates? => Equilibrium economics

• Complexity approach: how does behavior adapt toadapt to

the pattern it creates? => Out-of-equilibrium economics

Standard vs Complexity ApproachStandard vs Complexity Approach


Four Themes in Complexity EconomicsFour Themes in Complexity Economics

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

Hence such studies are evolutionary

2. Agents define the problem as they goHence cognition becomes important

3. Perpetual novelty is possibleBehavior may perpetually cause new structures

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


El FarolEl Farol

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100

Time

Numbers

Attending

Bar attendance in the first 100 weeks


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?

Documents

Complexity in the Economy and Business IBM Almaden Institute April 12, 2007 W. Brian Arthur External Professor, Santa Fe Institute