1. Complexity and the Nascent Revolution in Economics Lancaster University Dec 9, 2009 W. Brian Arthur External Professor, Santa Fe Institute

2. © 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 economy

3. © 2009 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. –(Usually with system being between order and chaos)

4. © 2009 W. Brian Arthur 4 The economy: naturally complex?

5. © 2009 W. Brian Arthur 5 Standard economics asks: What agent behavior is consistent with the pattern it creates? –“Solutions” are static equilibria => Equilibrium economics Complexity economics asks: How does behavior adapt to the pattern it creates? –Solutions are not necessarily equilibria => Nonequilibrium economics

6. © 2009 W. Brian Arthur 6 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?

7. © 2009 W. Brian Arthur 7 Equilibrium 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

8. © 2009 W. Brian Arthur 8 Nonequilibrium economics: themes 1.Agents define the problem as they go Hence 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 probabilistically May be multiple equilibria, one selected 4.Perpetual novelty is possible Behavior may perpetually cause new structures

9. © 2009 W. Brian Arthur 9 The Two Approaches: An Example Q. How do stock markets work? The Asset Pricing Problem

10. © 2009 W. Brian Arthur 10 Standard 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 11 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)}?

12. © 2009 W. Brian Arthur 12 SFI Artificial Stock Market (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?

13. © 2009 W. Brian Arthur 13 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?

14. © 2009 W. Brian Arthur 14 How 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

15. © 2009 W. Brian Arthur 15 Market StateForecast 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

16. © 2009 W. Brian Arthur 16 Market StateForecast 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

17. © 2009 W. Brian Arthur 17 We find: two regimes for the market 1. If updating (learning) rate is low –Convergence to the standard rational expectations equilibrium

18. © 2009 W. Brian Arthur 18 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

19. © 2009 W. Brian Arthur 19 Complexity economics: 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

20. © 2009 W. Brian Arthur 20 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

21. © 2009 W. Brian Arthur 21 In the real economy, all systems will be gamed … Russia’s big bang California’s freeing of the electricity market Wall Street’s derivatives built on derivatives

22. © 2009 W. Brian Arthur 22 Needed: strategic analysis of 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?

23. © 2009 W. Brian Arthur 23