Very Large-Scale Multi-Agent Systems and Emergent Macroeconomics Rob Axtell [email protected]...

Very Large-ScaleVery Large-ScaleMulti-Agent SystemsMulti-Agent SystemsandandEmergentEmergentMacroeconomicsMacroeconomics

Rob AxtellRob [email protected]@brookings.edu

Center on Social and Economic DynamicsCenter on Social and Economic Dynamics

The Brookings InstitutionThe Brookings Institution

Washington, D.C. USAWashington, D.C. USA

www.brookings.edu/dynamicswww.brookings.edu/dynamics CSED

OutlineOutline

Agent computingAgent computing in economics in economics and other fieldsand other fields

Artificial economiesArtificial economies of adaptive of adaptive agentsagents

The macroeconomy, The macroeconomy, emergentemergent Architecture of an Architecture of an artificial artificial

macroeconomymacroeconomy ConclusionsConclusions

CSED

Macro from Agents: Macro from Agents: BackgroundBackground

Microsimulation (e.g., Orcutt)Microsimulation (e.g., Orcutt) Small # of households (e.g., 16K memory) to all householdsSmall # of households (e.g., 16K memory) to all households No strategic behavior; essentially an accounting methodNo strategic behavior; essentially an accounting method

AspenAspen model from Sandia (mid 1990s) model from Sandia (mid 1990s) Super-computing applicationSuper-computing application Vague empirical relevanceVague empirical relevance

Extant macroeconomics with agentsExtant macroeconomics with agents Few agents (often 1 or 2!)Few agents (often 1 or 2!) Maximization of discounted expected utilityMaximization of discounted expected utility

‘‘Financial fragility’ models of Gallegati and co-Financial fragility’ models of Gallegati and co-workersworkers Exogenous shocksExogenous shocks Firms as agentsFirms as agents

Emerging NISAC infrastructureEmerging NISAC infrastructureCSED

Our MASs Macro ProjectOur MASs Macro Project

TeamTeam Agent-based microeconomics (R Axtell)Agent-based microeconomics (R Axtell)

Manage code specifications of component modelsManage code specifications of component models Macroeconomics (C Georges, A Leijonhufvud)Macroeconomics (C Georges, A Leijonhufvud)

Adaptive agent models in finance, international tradeAdaptive agent models in finance, international trade Veteran macroeconomists: provide critical Veteran macroeconomists: provide critical guidanceguidance

on both model on both model specificationspecification and reasonableness of and reasonableness of outputoutput

Computer science (K DeJong)Computer science (K DeJong) Multi-agent systems peopleMulti-agent systems people Learning specialistsLearning specialists Evolutionary computing prosEvolutionary computing pros

GoalsGoals Challenge representative agent macroChallenge representative agent macroCSED

Solitary vs Interactive Solitary vs Interactive AgentsAgents

SolitarySolitary Utility function holds Utility function holds

own state and global own state and global economic variableseconomic variables

Maximization done Maximization done without regard for without regard for others’ direct interests others’ direct interests (“passable definition of (“passable definition of a sociopath” [Aaron, a sociopath” [Aaron, 1994])1994])

Seeks global optimumSeeks global optimum Asocial or anti-social Asocial or anti-social

InteractiveInteractive Utility function holds Utility function holds

individual state, family, individual state, family, community, societal community, societal actions/welfareactions/welfare

Seeks own utility Seeks own utility improvements, welfare improvements, welfare for others (e.g., for others (e.g., fairness)fairness)

Adaptation through Adaptation through interactioninteraction

SocialSocial

CSED

Power of InteractionPower of Interaction

Paradigm of Paradigm of non-interactive non-interactive computing:computing: DataData MachineMachine (e.g., Turing machine) (e.g., Turing machine) Machine turns data into the answer (e.g., Machine turns data into the answer (e.g.,

4242) via ) via algorithmalgorithm Multi-agent systems: Multi-agent systems: interactiveinteractive

computingcomputing P Wegner: P Wegner: systems of interacting agentssystems of interacting agents at at

least as powerful as a Turing machineleast as powerful as a Turing machine Useful formulation for on-line MASUseful formulation for on-line MASCSED

Agent Computing in Agent Computing in EconomicsEconomics

Agents are the only way for economists Agents are the only way for economists to to fully utilizefully utilize modern hardware modern hardware Code a few classes of agents and replicateCode a few classes of agents and replicate ‘‘Small-compile time, large run-time’ modelSmall-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 Agent models can be considered as richerricher specificationsspecifications than typical than typical econometricseconometricsCSED

Artificial Agent Artificial Agent Economies as Multi-Level Economies as Multi-Level

SystemsSystems

Empirical relevance can be achieved at different levelsObservation: For macro we really have a 3 level system: agents (bottom),macro (top) and institutions (middle)

x(t) x(t+1)f: Rn Rn

y(t) y(t+1)g: Rm Rm

a: Rn Rm

m < n

Micro-dynamics

Macro-dynamics

CSED

Against the Nash Against the Nash ProgramProgram

An An implicitimplicit assumption of conventional assumption of conventional game theory is that social regularities arise game theory is that social regularities arise from equilibrium at the from equilibrium at the agent levelagent level

Clearly, this is Clearly, this is sufficientsufficient; it is ; it is notnot necessarynecessary Counter-examples: agent-based financial Counter-examples: agent-based financial

markets and firm formation modelsmarkets and firm formation models In a large population, agents perpetually In a large population, agents perpetually

adapt their behavior to one another and adapt their behavior to one another and their circumstances, yet stationary their circumstances, yet stationary structures can arise at the social levelstructures can arise at the social level

CSED

Conventional Conventional MacroeconomicsMacroeconomics

ReductionistReductionist perspective perspective Describe behavior of Describe behavior of

components components mathematicallymathematically (dynamical systems)(dynamical systems)

AggregateAggregate components to components to subsystems (e.g., financial, subsystems (e.g., financial, money, credit, social norms, money, credit, social norms, regulatory)regulatory)

Dynamical behavior of each Dynamical behavior of each subsystem subsystem veryvery complex complex

Link all subsystems Link all subsystems together and there is notogether and there is no analytical analytical (i.e., closed form) (i.e., closed form) representation of the whole representation of the whole economyeconomy

Workarounds…Workarounds… Physicists get around Physicists get around

this problem via this problem via homogeneity, homogeneity, then then statistical mechanicsstatistical mechanics

Engineers get around Engineers get around problem problem pragmaticallypragmatically via heuristics, rules-of-via heuristics, rules-of-thumb, computer thumb, computer models, multi-agent models, multi-agent organizationsorganizations

Macroeconomists use Macroeconomists use two main abstractions:two main abstractions: representative agent/firmrepresentative agent/firm aggregate dataaggregate data

Extant Work: Agents and Extant Work: Agents and MacroMacro

Arifovic, Bullard, Duffy, Georges, Arifovic, Bullard, Duffy, Georges, others:others: Relatively few agentsRelatively few agents Somewhat conventional macroeconomic Somewhat conventional macroeconomic

set-upsset-ups Focus on learning dynamics common Focus on learning dynamics common

(e.g, GA learning)(e.g, GA learning) Gallegati Gallegati et alet al.:.:

Credit market dynamicsCredit market dynamics Exogenous shocksExogenous shocks Emergent MacroeconomicsEmergent Macroeconomics

EmergentEmergent MacroeconomicsMacroeconomics

Dynamical models for all Dynamical models for all components of an components of an economyeconomy

Two flavors:Two flavors: Institutions as agentsInstitutions as agents Individuals as agents Individuals as agents

(institutions as MAS)(institutions as MAS) Explicitly specify inter-Explicitly specify inter-

actions between agentsactions between agents Spin the whole Spin the whole artificial artificial

economyeconomy forward in time; forward in time; equilibrium equilibrium agnosticismagnosticism

Aggregates Aggregates emergeemerge Emergent macrovariables Emergent macrovariables

influence agent behaviorinfluence agent behavior

Philosophy of Philosophy of EmergenceEmergence

Pragmatic anti-reductionismPragmatic anti-reductionism Aggregates and institutions arise from the Aggregates and institutions arise from the

interactionsinteractions of autonomous agents of autonomous agents Aggregates may be well-defined at both the Aggregates may be well-defined at both the

individual and social levels, e.g., savingsindividual and social levels, e.g., savings Institutions may have behavior not defined at Institutions may have behavior not defined at

the individual level (e.g., policy-setting ability)the individual level (e.g., policy-setting ability) A macroeconomy is a A macroeconomy is a complex adaptive complex adaptive

systemsystem Difficulties of the ‘representative agent’ are a Difficulties of the ‘representative agent’ are a

special case of the philosophers’ “fallacy of special case of the philosophers’ “fallacy of division”division”

Related to notions of ‘ecological inference’Related to notions of ‘ecological inference’

Macroeconomics from Macroeconomics from MicroMicro

‘‘Microfoundations of macro’ is Microfoundations of macro’ is conventionally interpreted as the Walrasian conventionally interpreted as the Walrasian foundationsfoundations

Historically, Walrasian model was criticized Historically, Walrasian model was criticized for being an ‘institution-free’ theoryfor being an ‘institution-free’ theory

Bottom-up/emergent macro has the same Bottom-up/emergent macro has the same aspirations but an alternative methodology:aspirations but an alternative methodology: ‘‘Grow’ macroeconomic aggregates from a Grow’ macroeconomic aggregates from a

heterogeneous population of boundedly rational heterogeneous population of boundedly rational agents who interact directly with one another, agents who interact directly with one another, away from equilibriumaway from equilibrium

Along the way ‘grow’ meso-scale institutionsAlong the way ‘grow’ meso-scale institutions Many microspecifications will likely prove Many microspecifications will likely prove

sufficient (although today we have none!)sufficient (although today we have none!)

Any Any ArtificialArtificial EconomyEconomy must must have…have…

Artificial Agents…Artificial Agents… ……have preferences, are consumershave preferences, are consumers ……earn wages in firms as workers, migrate between earn wages in firms as workers, migrate between

firmsfirms ……own shares of firmsown shares of firms

Artificial Firms…Artificial Firms… ……make products to sell to consumers and firmsmake products to sell to consumers and firms ……pay wages to workerspay wages to workers ……banks as special casebanks as special case

Artificial Markets…Artificial Markets… ……for consumption and capital goods, prices emergefor consumption and capital goods, prices emerge ……for ownership of firms, share prices emergefor ownership of firms, share prices emerge

Certain Certain institutionsinstitutions emergent… emergent… ……money, price level, exchange regimes, etc.money, price level, exchange regimes, etc. ……social norms of contracts, work effort and so onsocial norms of contracts, work effort and so on ……informal social networksinformal social networks

An Artificial EconomyAn Artificial Economy

Consumer behavior(Carroll and Allen [2001])


Firm formation(Axtell [1999, 2002]



Financial market(Lux or LeBaron)




Financial market(Lux or LeBaron)



Labor m

kts (Tesf

atsion)

Artificial Agents:Artificial Agents:Workers and ConsumersWorkers and Consumers

Preferences for consumption goods and Preferences for consumption goods and leisure, constrained by income, wealthleisure, constrained by income, wealth

Behavioral realism, e.g.Behavioral realism, e.g. non-exponential discountingnon-exponential discounting gain-loss asymmetrygain-loss asymmetry varying degrees of risk aversionvarying degrees of risk aversion

Seek (e.g., grope for) utility improvements Seek (e.g., grope for) utility improvements through consumption and work choicesthrough consumption and work choices

Varying degrees of myopia depending on Varying degrees of myopia depending on decision parametersdecision parameters

Weak empirical targetsWeak empirical targets

Artificial FirmsArtificial Firms Composed of agentsComposed of agents Each makes a single consumption Each makes a single consumption

goodgood Increasing returns to scale (effort)Increasing returns to scale (effort) Some compensation systemSome compensation system Non-cooperative behaviorNon-cooperative behavior Sales and profits, are determined by Sales and profits, are determined by

marketmarket Agents migrate between firms when Agents migrate between firms when

it is utility-improving to do soit is utility-improving to do so Solid empirical targetsSolid empirical targets

Artificial MarketsArtificial Markets Consumption, credit and capital goods:Consumption, credit and capital goods:

Single marketSingle market Many marketsMany markets

Labor ‘market’:Labor ‘market’: Single market with search costsSingle market with search costs Many marketsMany markets

Equity market:Equity market: Shares of firms bought and soldShares of firms bought and sold Price is endogenousPrice is endogenous Agents purchase shares with savingsAgents purchase shares with savings

Must forecast priceMust forecast price Must decide what to buy and sellMust decide what to buy and sell

Typical Set-UpTypical Set-Up 10107 7 agents with heterogeneous preferencesagents with heterogeneous preferences IC: all working as IC: all working as singletonssingletons Run overnight to wipe out initial transientRun overnight to wipe out initial transient Model output:Model output:

Fluctuating aggregate output, prices, real Fluctuating aggregate output, prices, real wages, unemployment rate, share priceswages, unemployment rate, share prices

Multi-agent firms Multi-agent firms emergeemerge skew (Pareto) size distributionskew (Pareto) size distribution heavy-tailed (Laplace) growth rate distributionheavy-tailed (Laplace) growth rate distribution wage-firm size effectwage-firm size effect

Stock market dynamics emergeStock market dynamics emerge heavy-tailed SR price fluctuations heavy-tailed SR price fluctuations Gaussian LR Gaussian LR clustered volatilityclustered volatility

Empirical Artificial Empirical Artificial EconomiesEconomies

Many levels:Many levels: ‘‘Sniff test’ by ‘old hands’Sniff test’ by ‘old hands’ CalibrationCalibration ‘‘Estimation by simulation’ Estimation by simulation’

in principlein principle Econometrics:Econometrics:

Agent models can be Agent models can be considered as considered as richerricher specificationsspecifications

Identification may be Identification may be problematicalproblematical

Community of agent-Community of agent-based computational based computational economists has too little economists has too little experience w/empirical experience w/empirical modelsmodels

Software DevelopmentSoftware Development Progressively add features, e.g.,Progressively add features, e.g.,

Richer specification of the credit marketRicher specification of the credit market Expand the role of moneyExpand the role of money

Getting institutions to emerge, e.g.,Getting institutions to emerge, e.g., Emergence of money (à la Howitt and Emergence of money (à la Howitt and

Clower)Clower) Parallel C++ and Java Parallel C++ and Java

implementationsimplementations Dissemination:Dissemination:

Open portal on the web so outsiders can Open portal on the web so outsiders can add their own agents?add their own agents?

Pegagogical toolPegagogical tool

Mass Macro:Mass Macro:Software ArchitectureSoftware Architecture

Philosophy: Economy composed of Philosophy: Economy composed of heterogeneous, interacting, heterogeneous, interacting, autonomous autonomous peoplepeople

Design: Represent people by Design: Represent people by heterogeneous, interacting, heterogeneous, interacting, autonomous software autonomous software agentsagents

Implementation: Distinct types of Implementation: Distinct types of agents as distinct classes of software agents as distinct classes of software objectsobjects

Ultimate GoalsUltimate Goals

101088 agents agents Emergent firmsEmergent firms Emergent moneyEmergent money Emergent products to satisfy Emergent products to satisfy

preferencespreferences Representation of governance Representation of governance

structuresstructures Macroeconomic statistics that resemble Macroeconomic statistics that resemble

real datareal data

Agent ClassAgent Class

Abstract agent

Worker agent Consumer agent

Agent

Firm ClassFirm 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

Economy ClassEconomy Class

Economy class

Firm population class

Firm object

Firm object

Firm object

Firm object

Agent population class

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Decentralized Markets:Decentralized Markets:Price Formation through Price Formation through

IntermediariesIntermediaries

Storeobject

Firmobject

Firmobject

Firmobject

Firmobject Firm

object

Consumeragent

Consumeragent

Consumeragent

Consumeragent

Consumeragent

Consumeragent

Storeobject

Data GatheringData Gathering

Economy class

Firm population class

Firm object

Firm object

Firm object

Firm object

Agent population class

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Agentobject

Data gathering classJournalists (ad hoc methods)

Statisticians (formal methods)

Parallelization IssuesParallelization Issues 101088 agents will require multiple machines agents will require multiple machines

(>100 bytes/agent, thus > 10(>100 bytes/agent, thus > 101010 bytes) bytes) Arbitrary inter-agent and agent-firm Arbitrary inter-agent and agent-firm

communication is too costly to permitcommunication is too costly to permit ‘‘Localized’ agent-agent communication Localized’ agent-agent communication

and ‘mail’ for long distance (across and ‘mail’ for long distance (across machine) communicationmachine) communication

Firm-agent communication mediated by Firm-agent communication mediated by ‘newspapers’, with each machine having ‘newspapers’, with each machine having at least one newspaper.at least one newspaper.

ConclusionsConclusions

Software architecture for massive multi-Software architecture for massive multi-agent systems approach to macro (aka agent systems approach to macro (aka bottom-up, emergent macro)bottom-up, emergent macro)

Beginning phase of multi-year projectBeginning phase of multi-year project Significant investment in software Significant investment in software

specification for broad applicabilityspecification for broad applicability Instantiations planned for real Instantiations planned for real

macroeconomiesmacroeconomies No real results yetNo real results yet

Main HurdlesMain Hurdles How to get How to get realistic institutionsrealistic institutions into such a into such a

model?model? Let them emerge…Let them emerge… ……or build them in?or build them in?

Evidence of our Evidence of our limited knowledgelimited knowledge of how of how agents form institutionsagents form institutions Ostrom: Emergence of Ostrom: Emergence of self-governanceself-governance

institutionsinstitutions HypothesesHypotheses::

Many other heretofore unknown difficultiesMany other heretofore unknown difficulties Satisfactory execution of this research program Satisfactory execution of this research program

will take decades!will take decades!

Main Casualties of the Artificial Main Casualties of the Artificial Economy Approach to MacroEconomy Approach to Macro

HomogeneityHomogeneity assumptions assumptions Good riddance!Good riddance!

Agents as Agents as omniscientomniscient utility maximizers utility maximizers Forthcoming marriage of artificial economies Forthcoming marriage of artificial economies

to experimental/behavioral economics?to experimental/behavioral economics? Economic agents as Economic agents as solitarysolitary actors actors

Hello sociologyHello sociology EquilibriumEquilibrium: against the Nash program: against the Nash program RepresentativeRepresentative anything: micro to macro anything: micro to macro

mediated by institutionsmediated by institutions Theoretically: the Theoretically: the corecore

SummarySummary LargeLarge--scalescale agent models are just agent models are just

about feasible todayabout feasible today Prior work on agent modeling of major Prior work on agent modeling of major

components of the economy exists and components of the economy exists and is sufficiently rich to synthesize into a is sufficiently rich to synthesize into a first generation first generation artificial economyartificial economy

This work will come to fruition over This work will come to fruition over next few yearsnext few years

A A new waynew way to do macro! to do macro! Main limitation is how to treat Main limitation is how to treat

institutionsinstitutions

Final Thoughts onFinal Thoughts onArtificial EconomiesArtificial Economies

OntologyOntology of mathematical economics is of mathematical economics is maximizationmaximization:: Given agent methodology, why Given agent methodology, why maximize?maximize? Are equations outside of agents Are equations outside of agents legitimatelegitimate??

Firms are multi-agent systems:Firms are multi-agent systems: Why Why singlesingle agent firms in agent models? agent firms in agent models? Who can get profit maximization to Who can get profit maximization to emergeemerge??

SensitivitySensitivity analysis and scalability issues: analysis and scalability issues: How do results depend on How do results depend on N?N?

Exciting Time forExciting Time forArtificial EconomiesArtificial Economies

Almost everything is an Almost everything is an openopen problemproblem:: How to ‘grow’…How to ‘grow’…

……the familythe family ……private propertyprivate property ……the Statethe State

How to regulate…How to regulate… ……a financial marketa 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 theoryAnalogy: Early days of game theory We have reached We have reached the end of the the end of the

beginning!beginning!

Artificial EconomicsArtificial Economics Forthcoming book: Forthcoming book:

Artificial Artificial Economies of Adaptive Agents: The Economies of Adaptive Agents: The Multi-Agent Systems Approach to Multi-Agent Systems Approach to EconomicsEconomics, 2006/2007, 2006/2007

Conference in Denmark Conference in Denmark in the fall (Charlotte Bruun): in the fall (Charlotte Bruun): www.socsci.aau.dk/ae2006/www.socsci.aau.dk/ae2006/

New European project on this New European project on this general theme: general theme: EurACEEurACE

Very Large-Scale Multi-Agent Systems and Emergent Macroeconomics Rob Axtell [email protected]...

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