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

2. © 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 economy

3. © 2007 W. Brian Arthur 3 What is complexity? Elements responding to the pattern their behavior co-creates –A concern with how things form from simpler elements

4. © 2007 W. Brian Arthur 4 The economy is naturally complex

5. © 2007 W. Brian Arthur 5 Standard economics asks: What agent behavior is consistent with the pattern it creates? “Solutions” are static equilibria –General equilibrium theory –Game theory –Rational expectations economics

6. © 2007 W. Brian Arthur 6 Complexity economics asks: How does behavior adapt to the pattern it creates? Solutions not necessarily in equilibrium Therefore a non-equilibrium economics

7. © 2007 W. Brian Arthur 7 Standard economics Need to model rationality of agents –Identical agents who use perfect rationality –Problem given and well-defined for agents –Equation based

8. © 2007 W. Brian Arthur 8 Non-equilibrium economics Need to model process of adjustment for agents –Possible perpetual novelty –“Cognitive agents” who may differ –Evolutionary setup natural –Algorithmic

9. © 2007 W. Brian Arthur 9 Standard economics based on diminishing returns (negative feedbacks) Keeps equilibrium unique

10. © 2007 W. Brian Arthur 10 Increasing returns problems difficult 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

11. © 2007 W. Brian Arthur 11 Dealing 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

12. © 2007 W. Brian Arthur 12 The Two Approaches: An Example SFI Artificial Stock Market Arthur, Holland, LeBaron, Palmer, Tayler (1997) How do stock markets work? –The Asset Pricing Problem

13. © 2007 W. Brian Arthur 13 Standard Theory of Asset Pricing Forecasting Machine: E[p(t+1)|I(t)] Market Maker Buy/Sell Orders Information I(t) p(t+1) Rational Expectations Equilibrium: What forecasting machine is on average validated by {p(t)}?

14. © 2007 W. Brian Arthur 14 Nonequilibrium Version Agents must form (possibly different) hypotheses to forecast Market Maker Buy/Sell Orders Information I(t) p(t+1) What will be market behavior? Will this settle to standard outcome?

15. © 2007 W. Brian Arthur 15 How 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

16. © 2007 W. Brian Arthur 16 We find: two regimes for the market 1. If updating (learning) rate is low –Convergence to the standard rational expectations equilibrium

17. © 2007 W. Brian Arthur 17 We 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

18. © 2007 W. Brian Arthur 18 Complexity economics: fad or paradigm shift? Sometimes convergence to standard equilibrium outcomes. Equilibrium economics a special case This is a generalization of standard economics

19. © 2007 W. Brian Arthur 19 Implications 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

20. © 2007 W. Brian Arthur 20 How does this apply in business? Seeing business from an ecological viewpoint Awareness of defining problem as you go

21. © 2007 W. Brian Arthur 21 How does this apply in business? Planning. But allowing some structures to “emerge” Providing “libraries” of solutions

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24. © 2007 W. Brian Arthur 24 Example: 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

25. © 2007 W. Brian Arthur 25 El Farol --how agents learn The bar-goers form hypotheses about the problem and act on currently most accurate of these n “ecology” of beliefs emerges. Changes over time An “ecology” of beliefs emerges. Changes over time I.e. a “psychology” of the market emerges

26. © 2007 W. Brian Arthur 26 consistent withStandard economics: what behavior is consistent with the pattern it creates? => Equilibrium economics adapt toComplexity approach: how does behavior adapt to the pattern it creates? => Out-of-equilibrium economics Standard vs Complexity Approach

27. © 2007 W. Brian Arthur 27 Four 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 go Hence cognition becomes important 3.Perpetual novelty is possible Behavior may perpetually cause new structures 4.Structures “emerge” or are selected probabilistically May be multiple equilibria, one selected

28. © 2007 W. Brian Arthur 28 El Farol Bar attendance in the first 100 weeks

29. © 2007 W. Brian Arthur 29 Equilibria: 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?