Statistical Challenges in Agent-Based
Computational Modeling
László Gulyás ([email protected])AITIA International Inc &Lorand Eötvös University, Budapest
Gulyás László 2
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
Gulyás László 3
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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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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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 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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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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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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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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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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Verification & Validation
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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Socio-Geographic Network=1.9284, L=2.5062, Seed 1
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hare Transit
Bicycle
Car
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Socio-Geographic Network=1.9075, L=1, Seed 2
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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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Verification & Validation
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.
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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.
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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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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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