1. Very Large-Scale Multi-Agent Systems and Emergent Macroeconomics Rob Axtell raxtell@brookings.edu Center on Social and Economic Dynamics The Brookings Institution Washington, D.C. USA www.brookings.edu/dynamics CSED

2. Outline Agent computing in economics and other fields Agent computing in economics and other fields Artificial economies of adaptive agents Artificial economies of adaptive agents The macroeconomy, emergent The macroeconomy, emergent Architecture of an artificial macroeconomy Architecture of an artificial macroeconomy Conclusions Conclusions CSED

3. Macro from Agents: Background Microsimulation (e.g., Orcutt) Microsimulation (e.g., Orcutt) Small # of households (e.g., 16K memory) to all households Small # of households (e.g., 16K memory) to all households No strategic behavior; essentially an accounting method No strategic behavior; essentially an accounting method Aspen model from Sandia (mid 1990s) Aspen model from Sandia (mid 1990s) Super-computing application Super-computing application Vague empirical relevance Vague empirical relevance Extant macroeconomics with agents Extant macroeconomics with agents Few agents (often 1 or 2!) Few agents (often 1 or 2!) Maximization of discounted expected utility Maximization of discounted expected utility ‘Financial fragility’ models of Gallegati and co-workers ‘Financial fragility’ models of Gallegati and co-workers Exogenous shocks Exogenous shocks Firms as agents Firms as agents Emerging NISAC infrastructure Emerging NISAC infrastructure CSED

4. Our MASs Macro Project Team Team Agent-based microeconomics (R Axtell) Agent-based microeconomics (R Axtell) Manage code specifications of component models Manage code specifications of component models Macroeconomics (C Georges, A Leijonhufvud) Macroeconomics (C Georges, A Leijonhufvud) Adaptive agent models in finance, international trade Adaptive agent models in finance, international trade Veteran macroeconomists: provide critical guidance on both model specification and reasonableness of output Veteran macroeconomists: provide critical guidance on both model specification and reasonableness of output Computer science (K DeJong) Computer science (K DeJong) Multi-agent systems people Multi-agent systems people Learning specialists Learning specialists Evolutionary computing pros Evolutionary computing pros Goals Goals Challenge representative agent macro Challenge representative agent macro CSED

5. Solitary vs Interactive Agents Solitary Solitary Utility function holds own state and global economic variables Utility function holds own state and global economic variables Maximization done without regard for others’ direct interests (“passable definition of a sociopath” [Aaron, 1994]) Maximization done without regard for others’ direct interests (“passable definition of a sociopath” [Aaron, 1994]) Seeks global optimum Seeks global optimum Asocial or anti-social Asocial or anti-social Interactive Utility function holds individual state, family, community, societal actions/welfare Seeks own utility improvements, welfare for others (e.g., fairness) Adaptation through interaction Social CSED

6. Power of Interaction Paradigm of non-interactive computing: Paradigm of non-interactive computing: Data Data Machine (e.g., Turing machine) Machine (e.g., Turing machine) Machine turns data into the answer (e.g., 42) via algorithm Machine turns data into the answer (e.g., 42) via algorithm Multi-agent systems: interactive computing Multi-agent systems: interactive computing P Wegner: systems of interacting agents at least as powerful as a Turing machine P Wegner: systems of interacting agents at least as powerful as a Turing machine Useful formulation for on-line MAS Useful formulation for on-line MAS CSED

7. Agent Computing in Economics Agents are the only way for economists to fully utilize modern hardware Agents are the only way for economists to fully utilize modern hardware Code a few classes of agents and replicate Code a few classes of agents and replicate ‘Small-compile time, large run-time’ model ‘Small-compile time, large run-time’ model No way fill 1 GB RAM with equations! No way fill 1 GB RAM with equations! Agent models can be considered as richer specifications than typical econometrics Agent models can be considered as richer specifications than typical econometrics CSED

8. Artificial Agent Economies as Multi-Level Systems Empirical relevance can be achieved at different levels Observation: For macro we really have a 3 level system: agents (bottom), macro (top) and institutions (middle) x(t) x(t+1) f: R n RnRn y(t) y(t+1) g: R m RmRm a: R n RmRm m < n Micro-dynamics Macro-dynamics CSED

9. Against the Nash Program An implicit assumption of conventional game theory is that social regularities arise from equilibrium at the agent level An implicit assumption of conventional game theory is that social regularities arise from equilibrium at the agent level Clearly, this is sufficient; it is not necessary Clearly, this is sufficient; it is not necessary Counter-examples: agent-based financial markets and firm formation models Counter-examples: agent-based financial markets and firm formation models In a large population, agents perpetually adapt their behavior to one another and their circumstances, yet stationary structures can arise at the social level In a large population, agents perpetually adapt their behavior to one another and their circumstances, yet stationary structures can arise at the social level CSED

10. Conventional Macroeconomics Reductionist perspective Reductionist perspective Describe behavior of components mathematically (dynamical systems) Describe behavior of components mathematically (dynamical systems) Aggregate components to subsystems (e.g., financial, money, credit, social norms, regulatory) Aggregate components to subsystems (e.g., financial, money, credit, social norms, regulatory) Dynamical behavior of each subsystem very complex Dynamical behavior of each subsystem very complex Link all subsystems together and there is no analytical (i.e., closed form) representation of the whole economy Link all subsystems together and there is no analytical (i.e., closed form) representation of the whole economy

11. Workarounds… Physicists get around this problem via homogeneity, then statistical mechanics Engineers get around problem pragmatically via heuristics, rules-of-thumb, computer models, multi- agent organizations Macroeconomists use two main abstractions: representative agent/firm aggregate data

12. Extant Work: Agents and Macro Arifovic, Bullard, Duffy, Georges, others: Arifovic, Bullard, Duffy, Georges, others: Relatively few agents Relatively few agents Somewhat conventional macroeconomic set- ups Somewhat conventional macroeconomic set- ups Focus on learning dynamics common (e.g, GA learning) Focus on learning dynamics common (e.g, GA learning) Gallegati et al.: Gallegati et al.: Credit market dynamics Credit market dynamics Exogenous shocks Exogenous shocks Emergent Macroeconomics Emergent Macroeconomics

13. Emergent Macroeconomics Dynamical models for all components of an economy Dynamical models for all components of an economy Two flavors: Two flavors: Institutions as agents Institutions as agents Individuals as agents (institutions as MAS) Individuals as agents (institutions as MAS) Explicitly specify inter- actions between agents Explicitly specify inter- actions between agents Spin the whole artificial economy forward in time; equilibrium agnosticism Spin the whole artificial economy forward in time; equilibrium agnosticism Aggregates emerge Aggregates emerge Emergent macrovariables influence agent behavior Emergent macrovariables influence agent behavior

14. Philosophy of Emergence Pragmatic anti-reductionism Pragmatic anti-reductionism Aggregates and institutions arise from the interactions of autonomous agents Aggregates and institutions arise from the interactions of autonomous agents Aggregates may be well-defined at both the individual and social levels, e.g., savings Aggregates may be well-defined at both the individual and social levels, e.g., savings Institutions may have behavior not defined at the individual level (e.g., policy-setting ability) Institutions may have behavior not defined at the individual level (e.g., policy-setting ability) A macroeconomy is a complex adaptive system A macroeconomy is a complex adaptive system Difficulties of the ‘representative agent’ are a special case of the philosophers’ “fallacy of division” Difficulties of the ‘representative agent’ are a special case of the philosophers’ “fallacy of division” Related to notions of ‘ecological inference’ Related to notions of ‘ecological inference’

15. Macroeconomics from Micro ‘Microfoundations of macro’ is conventionally interpreted as the Walrasian foundations ‘Microfoundations of macro’ is conventionally interpreted as the Walrasian foundations Historically, Walrasian model was criticized for being an ‘institution-free’ theory Historically, Walrasian model was criticized for being an ‘institution-free’ theory Bottom-up/emergent macro has the same aspirations but an alternative methodology: Bottom-up/emergent macro has the same aspirations but an alternative methodology: ‘Grow’ macroeconomic aggregates from a heterogeneous population of boundedly rational agents who interact directly with one another, away from equilibrium ‘Grow’ macroeconomic aggregates from a heterogeneous population of boundedly rational agents who interact directly with one another, away from equilibrium Along the way ‘grow’ meso-scale institutions Along the way ‘grow’ meso-scale institutions Many microspecifications will likely prove sufficient (although today we have none!) Many microspecifications will likely prove sufficient (although today we have none!)

16. Any Artificial Economy must have… Artificial Agents… Artificial Agents… …have preferences, are consumers …have preferences, are consumers …earn wages in firms as workers, migrate between firms …earn wages in firms as workers, migrate between firms …own shares of firms …own shares of firms Artificial Firms… Artificial Firms… …make products to sell to consumers and firms …make products to sell to consumers and firms …pay wages to workers …pay wages to workers …banks as special case …banks as special case Artificial Markets… Artificial Markets… …for consumption and capital goods, prices emerge …for consumption and capital goods, prices emerge …for ownership of firms, share prices emerge …for ownership of firms, share prices emerge Certain institutions emergent… Certain institutions emergent… …money, price level, exchange regimes, etc. …money, price level, exchange regimes, etc. …social norms of contracts, work effort and so on …social norms of contracts, work effort and so on …informal social networks …informal social networks

17. An Artificial Economy Consumer behavior (Carroll and Allen [2001])

18. An Artificial Economy Firm formation (Axtell [1999, 2002] Consumer behavior (Carroll and Allen [2001])

19. An Artificial Economy Financial market (Lux or LeBaron) Firm formation (Axtell [1999, 2002] Consumer behavior (Carroll and Allen [2001])

20. An Artificial Economy Financial market (Lux or LeBaron) Firm formation (Axtell [1999, 2002] Consumer behavior (Carroll and Allen [2001]) Labor mkts (Tesfatsion)

21. Artificial Agents: Workers and Consumers Preferences for consumption goods and leisure, constrained by income, wealth Preferences for consumption goods and leisure, constrained by income, wealth Behavioral realism, e.g. Behavioral realism, e.g. non-exponential discounting non-exponential discounting gain-loss asymmetry gain-loss asymmetry varying degrees of risk aversion varying degrees of risk aversion Seek (e.g., grope for) utility improvements through consumption and work choices Seek (e.g., grope for) utility improvements through consumption and work choices Varying degrees of myopia depending on decision parameters Varying degrees of myopia depending on decision parameters Weak empirical targets Weak empirical targets

22. Artificial Firms Composed of agents Composed of agents Each makes a single consumption good Each makes a single consumption good Increasing returns to scale (effort) Increasing returns to scale (effort) Some compensation system Some compensation system Non-cooperative behavior Non-cooperative behavior Sales and profits, are determined by market Sales and profits, are determined by market Agents migrate between firms when it is utility-improving to do so Agents migrate between firms when it is utility-improving to do so Solid empirical targets Solid empirical targets

23. Artificial Markets Consumption, credit and capital goods: Consumption, credit and capital goods: Single market Single market Many markets Many markets Labor ‘market’: Labor ‘market’: Single market with search costs Single market with search costs Many markets Many markets Equity market: Equity market: Shares of firms bought and sold Shares of firms bought and sold Price is endogenous Price is endogenous Agents purchase shares with savings Agents purchase shares with savings Must forecast price Must forecast price Must decide what to buy and sell Must decide what to buy and sell

24. Typical Set-Up 10 7 agents with heterogeneous preferences 10 7 agents with heterogeneous preferences IC: all working as singletons IC: all working as singletons Run overnight to wipe out initial transient Run overnight to wipe out initial transient Model output: Model output: Fluctuating aggregate output, prices, real wages, unemployment rate, share prices Fluctuating aggregate output, prices, real wages, unemployment rate, share prices Multi-agent firms emerge Multi-agent firms emerge skew (Pareto) size distribution skew (Pareto) size distribution heavy-tailed (Laplace) growth rate distribution heavy-tailed (Laplace) growth rate distribution wage-firm size effect wage-firm size effect Stock market dynamics emerge Stock market dynamics emerge heavy-tailed SR price fluctuations  Gaussian LR heavy-tailed SR price fluctuations  Gaussian LR clustered volatility clustered volatility

25. Empirical Artificial Economies Many levels: Many levels: ‘Sniff test’ by ‘old hands’ ‘Sniff test’ by ‘old hands’ Calibration Calibration ‘Estimation by simulation’ in principle ‘Estimation by simulation’ in principle Econometrics: Econometrics: Agent models can be considered as richer specifications Agent models can be considered as richer specifications Identification may be problematical Identification may be problematical Community of agent-based computational economists has too little experience w/empirical models Community of agent-based computational economists has too little experience w/empirical models

26. Software Development Progressively add features, e.g., Progressively add features, e.g., Richer specification of the credit market Richer specification of the credit market Expand the role of money Expand the role of money Getting institutions to emerge, e.g., Getting institutions to emerge, e.g., Emergence of money (à la Howitt and Clower) Emergence of money (à la Howitt and Clower) Parallel C++ and Java implementations Parallel C++ and Java implementations Dissemination: Dissemination: Open portal on the web so outsiders can add their own agents? Open portal on the web so outsiders can add their own agents? Pegagogical tool Pegagogical tool

27. Mass Macro: Software Architecture Philosophy: Economy composed of heterogeneous, interacting, autonomous people Philosophy: Economy composed of heterogeneous, interacting, autonomous people Design: Represent people by heterogeneous, interacting, autonomous software agents Design: Represent people by heterogeneous, interacting, autonomous software agents Implementation: Distinct types of agents as distinct classes of software objects Implementation: Distinct types of agents as distinct classes of software objects

28. Ultimate Goals 10 8 agents 10 8 agents Emergent firms Emergent firms Emergent money Emergent money Emergent products to satisfy preferences Emergent products to satisfy preferences Representation of governance structures Representation of governance structures Macroeconomic statistics that resemble real data Macroeconomic statistics that resemble real data

29. Agent Class Abstract agent Worker agentConsumer agent Agent

30. Firm Class Firm: -Agent workers -Residual claimant -Production specification: --current output --production forecast -Compensation system Agent n Agent n-1 Agent i Agent 3 Agent 2 Agent 1

31. Economy Class Economy class Firm population class Firm object Agent population class Agent object Agent object Agent object Agent object Agent object Agent object Agent object Agent object Agent object

32. Decentralized Markets: Price Formation through Intermediaries Store object Firm object Firm object Firm object Firm object Firm object Consumer agent Consumer agent Consumer agent Consumer agent Consumer agent Consumer agent Store object

33. Data Gathering Economy class Firm population class Firm object Agent population class Agent object Agent object Agent object Agent object Agent object Agent object Agent object Agent object Agent object Data gathering class Journalists (ad hoc methods) Statisticians (formal methods)

34. Parallelization Issues 10 8 agents will require multiple machines (>100 bytes/agent, thus > 10 10 bytes) 10 8 agents will require multiple machines (>100 bytes/agent, thus > 10 10 bytes) Arbitrary inter-agent and agent-firm communication is too costly to permit Arbitrary inter-agent and agent-firm communication is too costly to permit ‘Localized’ agent-agent communication and ‘mail’ for long distance (across machine) communication ‘Localized’ agent-agent communication and ‘mail’ for long distance (across machine) communication Firm-agent communication mediated by ‘newspapers’, with each machine having at least one newspaper. Firm-agent communication mediated by ‘newspapers’, with each machine having at least one newspaper.

35. Conclusions Software architecture for massive multi-agent systems approach to macro (aka bottom-up, emergent macro) Software architecture for massive multi-agent systems approach to macro (aka bottom-up, emergent macro) Beginning phase of multi-year project Beginning phase of multi-year project Significant investment in software specification for broad applicability Significant investment in software specification for broad applicability Instantiations planned for real macroeconomies Instantiations planned for real macroeconomies No real results yet No real results yet

36. Main Hurdles How to get realistic institutions into such a model? How to get realistic institutions into such a model? Let them emerge… Let them emerge… …or build them in? …or build them in? Evidence of our limited knowledge of how agents form institutions Evidence of our limited knowledge of how agents form institutions Ostrom: Emergence of self-governance institutions Ostrom: Emergence of self-governance institutions Hypotheses: Hypotheses: Many other heretofore unknown difficulties Many other heretofore unknown difficulties Satisfactory execution of this research program will take decades! Satisfactory execution of this research program will take decades!

37. Main Casualties of the Artificial Economy Approach to Macro Homogeneity assumptions Homogeneity assumptions Good riddance! Good riddance! Agents as omniscient utility maximizers Agents as omniscient utility maximizers Forthcoming marriage of artificial economies to experimental/behavioral economics? Forthcoming marriage of artificial economies to experimental/behavioral economics? Economic agents as solitary actors Economic agents as solitary actors Hello sociology Hello sociology Equilibrium: against the Nash program Equilibrium: against the Nash program Representative anything: micro to macro mediated by institutions Representative anything: micro to macro mediated by institutions Theoretically: the core Theoretically: the core

38. Summary Large-scale agent models are just about feasible today Large-scale agent models are just about feasible today Prior work on agent modeling of major components of the economy exists and is sufficiently rich to synthesize into a first generation artificial economy Prior work on agent modeling of major components of the economy exists and is sufficiently rich to synthesize into a first generation artificial economy This work will come to fruition over next few years This work will come to fruition over next few years A new way to do macro! A new way to do macro! Main limitation is how to treat institutions Main limitation is how to treat institutions

39. Final Thoughts on Artificial Economies Ontology of mathematical economics is maximization: Ontology of mathematical economics is maximization: Given agent methodology, why maximize? Given agent methodology, why maximize? Are equations outside of agents legitimate? Are equations outside of agents legitimate? Firms are multi-agent systems: Firms are multi-agent systems: Why single agent firms in agent models? Why single agent firms in agent models? Who can get profit maximization to emerge? Who can get profit maximization to emerge? Sensitivity analysis and scalability issues: Sensitivity analysis and scalability issues: How do results depend on N? How do results depend on N?

40. Exciting Time for Artificial Economies Almost everything is an open problem: Almost everything is an open problem: How to ‘grow’… How to ‘grow’… …the family …the family …private property …private property …the State …the State How to regulate… How to regulate… …a financial market …a financial market …a multi-agent firm (e.g., environment) …a multi-agent firm (e.g., environment) …a macro-economy (i.e., not optimal control!) …a macro-economy (i.e., not optimal control!) Analogy: Early days of game theory Analogy: Early days of game theory We have reached the end of the beginning! We have reached the end of the beginning!

41. Artificial Economics Forthcoming book: Artificial Economies of Adaptive Agents: The Multi-Agent Systems Approach to Economics, 2006/2007 Forthcoming book: Artificial Economies of Adaptive Agents: The Multi-Agent Systems Approach to Economics, 2006/2007 Conference in Denmark in the fall (Charlotte Bruun): www.socsci.aau.dk/ae2006/ Conference in Denmark in the fall (Charlotte Bruun): www.socsci.aau.dk/ae2006/ www.socsci.aau.dk/ae2006/ New European project on this general theme: EurACE New European project on this general theme: EurACE