Statistical Challenges in Agent-Based Computational Modeling László Gulyás...

Statistical Challenges in Agent-Based

Computational Modeling

László Gulyás ([email protected])AITIA International Inc &Lorand Eötvös University, Budapest

mailto:[email protected]

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Overview On Agent-Based Modeling (ABM)

Properties, Praise & Critique Example

ABMs as Stochastic Processes Source of Randomness Basic ABM Methodology

Verification & Validation Challenges & Directions Networks

Example Experimental Validation

Example

Conclusions

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Example

Conclusions

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On Agent-Based Modeling (ABM) Main Properties

Bottom-Up Individuals with their idiosyncrasies, With their imperfections

(e.g., cognitive or computational limitations) Heterogeneous Populations Dynamic Populations Explicit Modeling of Interaction Topologies

Examples Santa Fe Institute Artificial Stock Market Discrete Choices on Networks

(Social Influence Modeling)

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Praise of ABM Attempt to Create Micro-Macro Links

“Micromotives and Macrobehavior”

Generative Modeling Approach

Realistic Microstructures Explicit Representation of Agents Realistic Computational Abilities Modeling of the Information Flow

Tool for Non-Equilibrium Behavior Ability to Study Trajectories

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Critique of ABM (Mis)Uses of Computer Simulation

Prediction………………………… (Weather) “Simulation”……………………..(Wright Bros) Thought Experiments /………(Evol of Coop.)

Existence Proofs

Computational (In)Efficiency

Questionable Results / Foundations?

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Example

Conclusions

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Example I.

The Santa Fe Institute Artificial Stock Market (SFI ASM)(Arthur et al., 1994, 1997)

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The Santa Fe Institute Artificial Stock Market (1/3)

A minimalist model of two assets: “Money”: fixed, risk-free, infinite supply,

fixed interest. “Stock”: unknown, risky behavior, finite

supply, varying dividend.

Artificial traders Developing (learning) trading strategies. In an attempt to maximize their wealth.

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The Santa Fe Institute Artificial Stock Market (2/3) Trading rules of the agents

Actions (buy, sell, hold) based on market indicators:

Fundamental and Technical Indicators Price > Fundamental Value, or Price < 100-period Moving Average, etc.

Reinforced if their ‘advice’ would have yielded profit.

A classifier system.

A Genetic algorithm Activated in random intervals

(individually for each agent). Replaces 10-20% of weakest the rules.

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The Santa Fe Institute Artificial Stock Market (3/3) Two behavioral regimes

(depending on learning speed).

One (Fundamental Trading) – Theory Consistent with Rational Expectations

Equilibrium. Price follows fundamental value of stock. Trading volume is low.

Two (Technical/Chartist Trading) – Practice “Chaotic” market behavior. “Bubbles” and “crashes”: price oscillates

around FV. Trading volume shows wild oscillations. “In accordance” with actual market behavior.

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Example

Conclusions

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ABMs as Stochastic Processes Not modeled processes are

typically represented by stochastic elements.

ABMs are implemented as Discrete Time Discrete Event simulations.

Markov Processes

Often with enormous state-spaces…

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ABM Methodology (101) High dimensionality of the parameter

space.

Only sampling is possible.

Establishing results’ independence from pseudo-random number sequences.

Sensitivity analysis, wrt. Parameters Pseudo-Random Number Sequences

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Example

Conclusions

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Verification & Validation

Challenges The Challenge of ‘Dimension

Collapse’ ANTs (John H. Miller) QosCosGrid EMIL

Empirical Fitting Micro- and Macro-Level Data Network Data Estimation Problems (Endogeneity)

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Directions I. Networks

Research on Network Data Collection Abstract Network Classes Empirically Grounded Abstract

Networks

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Example II.

Socio-Dynamic Discrete Choices on Networks in Space(Dugundji & Gulyas, 2002-2006)

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Starting Point

Discrete Choice Theory allows prediction based on computed individual choice probabilities for heterogeneous agents’ evaluation of discrete alternatives.

Individual choice probabilities are aggregated for policy forecasting.

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Industry Standard in Land Use Transportation Planning Models

Ground-breaking work: Ben-Akiva (1973); Lerman (1977)

Some operational models: Wegener (1998, IRPUD – Dortmund) Anas (1999, MetroSim – New York City) Hensher (2001, TRESIS – Sydney) Waddell (2002, UrbanSim – Salt Lake

City)

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Interdependence of Decision-Makers’ Choices Discrete Choice Theory is fundamentally

grounded in individual choice, however... Global versus local versus random

interactions Interaction through complex networks Network evolution

Problem domain: residential choice behavior and multi-modal transportation planning Social networks, transportation land use

networks

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Discrete Choice Model Population of N decision-making agents

indexed (1,...,n,...,N)

Each agent is faced with a single choice among mutually exclusive elemental alternatives i in the composite choice set C = {C1,...,CM}

For sake of simplicity, we assume that the (composite) choice set does not vary in size or content across agents.

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Nested Logit Models

1 2 ... m ... Mn

Lm

12 ... JC1 12 ... JCm 12 ... JCM

1 2

'

1

, ,...,

, '

( , ) ( | ) ( ) ( | ) ( )

M

m m

M

mm

n n m n n n

C C C C

C C m m

C C

P i m P i C P m P i m P m

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We introduce (social) network dynamics by allowing the systematic utilities Vin and Vmn to be linear-in-parameter first order functions of the proportions xin and xmn of a given decision-maker’s “reference entity” agents making these choices

Interaction Effects

...

...

iin i in i in

i

mmn m mn m mn

m

hV f x x

hV f x x

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Empirical Dilemma In practice…

It can be difficult to reveal the exact details of the relevant network(s) of reference entities influencing the choice of each decision-maker

The actual reference entities for a given decision-maker may not be among those in the data sample

One solution: studying abstract network classes with an

aim towards mathematical understanding of the properties of the model.

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Computational Model in RePast

(a) = 0.03, Random seed = 1

(b) = 5, Random seed = 1 (c) = 5, Random seed = 3

Example time series for 100 agents with f(x) = x for (a) low certainty

and (b), (c) high certainty with two distinct random seeds

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Results(Random / Erdős-Rényi network)

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Results(Watts-Strogatz network)

Empirical Application

Socio-Geographic Network

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Visualization of Semi-Abstract Socio-Geographic Network

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Socio-Geographic Network=1.9284, L=2.5062, Seed 1

0,0

0,1

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0,9

1,0

0 100000 200000 300000 400000 500000 600000

Time Step

Mod

e S

hare Transit

Bicycle

Car

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Socio-Geographic Network=1.9075, L=1, Seed 2

0,0

0,1

0,2

0,3

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0 100000 200000 300000 400000 500000 600000

Time Step

Mod

e S

hare Transit

Bicycle

Car

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Challenge in Estimation

Endogeneity!

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Example

Conclusions

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Directions II. Experimental Validation Participatory Simulation

The case of the SFI-ASM

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Example III.

The Participatory SFI-ASM(Gulyás, Adamcsek and Kiss, 2003, 2004.)

Can agents adapt to external trading strategies, just as well as they did to those developed by fellow agents?

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Humans Increase Market Volatility

The presence of human traders increased market volatility.

The higher percentage of the population was human, the higher the difference was w.r.t. the performance of the fully computational population.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

1 1001

Time period

8%

0%

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Participants Learn Fundamental Trading

First set of Experiments:

Humans initially applied technical trading, but gradually discovered fundamental strategies.

The winning human’s strategy was:

Buy if price < FV, sell otherwise.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 1001

Time period

Nor

mal

ized

Wea

lth

MinComp

AvgComp

MaxComp

MinHuman

AvgHuman

MaxHuman

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Artificial Chartist Agents

Second set of Experiments:

We introduced artificial chartist (technical) agents.

Base experiments show: Chartist agents normally increase market

volatility.

That is, humans are subjected to extreme bubbles and crashes.

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Participants Learn Technical Trading

Subjects received a bias towards fundamental indicators.

Still, they reported gradually switching for technical strategies after confronting with the ‘chartist’ market.

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Participants Moderate Market Deviations

However, chartist human subjects actually modulated the market’s volatility.

The market actually show REE-like behavior. The absolute winner’s strategy in this

case was a pure technical rule.

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Hypothesis

The learning rate again. The participants may have adapted

quicker.

The effect of human ‘impatience’. Cf. ‘Black Monday’ due to programmed

trading. An apparent lesson:

learning agents may do no better.

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Example

Conclusions

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Conclusions A methodology attempting the micro-

macro link: ABM.

Methodological challenges of ABM Mainly in empirical validation. Some in parameter space sampling.

Two new directions discussed Empirical estimation based on

semi-abstract networks. Participatory experiments.

Statistical Challenges in Agent-Based Computational Modeling László Gulyás...

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