Statistical Challenges in
Agent-Based
Computational Modeling
László Gulyás ([email protected])
AITIA International Inc &
Lorand Eötvös University, Budapest
Overview

On Agent-Based Modeling (ABM)



ABMs as Stochastic Processes



Properties, Praise & Critique
Example
Source of Randomness
Basic ABM Methodology
Verification & Validation


Challenges & Directions
Networks


Experimental Validation


Example
Example
Conclusions
Gulyás László
2
Overview

On Agent-Based Modeling (ABM)



ABMs as Stochastic Processes



Properties, Praise & Critique
Example
Source of Randomness
Basic ABM Methodology
Verification & Validation


Challenges & Directions
Networks


Experimental Validation


Example
Example
Conclusions
Gulyás László
3
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)
Gulyás László
4
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
Gulyás László
5
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?
Gulyás László
6
Overview

On Agent-Based Modeling (ABM)



ABMs as Stochastic Processes



Properties, Praise & Critique
Example
Source of Randomness
Basic ABM Methodology
Verification & Validation


Challenges & Directions
Networks


Experimental Validation


Example
Example
Conclusions
Gulyás László
7
Example I.

The Santa Fe Institute Artificial Stock
Market (SFI ASM)
(Arthur et al., 1994, 1997)
Gulyás László
8
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.
Gulyás László
9
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.
Gulyás László
10
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.
Gulyás László
11
Overview

On Agent-Based Modeling (ABM)



ABMs as Stochastic Processes



Properties, Praise & Critique
Example
Source of Randomness
Basic ABM Methodology
Verification & Validation


Challenges & Directions
Networks


Experimental Validation


Example
Example
Conclusions
Gulyás László
12
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…
Gulyás László
13
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
Gulyás László
14
Overview

On Agent-Based Modeling (ABM)



ABMs as Stochastic Processes



Properties, Praise & Critique
Example
Source of Randomness
Basic ABM Methodology
Verification & Validation


Challenges & Directions
Networks


Experimental Validation


Example
Example
Conclusions
Gulyás László
15
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)
Gulyás László
16
Verification & Validation

Directions I.

Networks
 Research
on Network Data Collection
 Abstract Network Classes
 Empirically Grounded Abstract Networks
Gulyás László
17
Example II.

Socio-Dynamic Discrete Choices on
Networks in Space
(Dugundji & Gulyas, 2002-2006)
Gulyás László
18
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.

Gulyás László
20
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)
Gulyás László
21
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
Gulyás László
22
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.
Gulyás László
23
Nested Logit Models
m
1
2
m
...
12 ... JC1
12 ... JCm
...
Mn
mLm
12 ... JCM
C  C1 , C2 ,..., CM 
Cm
M
m 1
Cm '   , m  m '
Cm  C
Pn (i, m)  Pn (i | Cm )  Pn (m)  Pn (i | m)  Pn (m)
Gulyás László
24
Interaction Effects

We introduce (social) network dynamics by
allowing the systematic utilities Vin and Vmn to be
linear-in-parameter b first order functions of the
proportions xin and xmn of a given decision-maker’s
“reference entity” agents making these choices
 hi

Vin  bi f  xin   bi 
 xin  ... 
 bi

Vmn
 hm

 b m f  xmn   b m 
 xmn  ... 
 bm

Gulyás László
27
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.
Gulyás László
28
Computational Model in RePast
(a) b = 0.03, Random seed = 1
(b) b = 5, Random seed = 1
(c) b = 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
Gulyás László
29
Results
(Random / Erdős-Rényi network)
Gulyás László
30
Results
(Watts-Strogatz network)
Gulyás László
31
Empirical Application
Socio-Geographic Network
Visualization of Semi-Abstract
Socio-Geographic Network
Gulyás László
34
Socio-Geographic Network
b=1.9284, m L=2.5062, Seed 1
1,0
0,9
Mode Share
0,8
0,7
0,6
Transit
0,5
Bicycle
0,4
Car
0,3
0,2
0,1
0,0
0
100000 200000 300000 400000 500000 600000
Time Step
Gulyás László
35
Socio-Geographic Network
b=1.9075, m L=1, Seed 2
1,0
0,9
Mode Share
0,8
0,7
0,6
Transit
0,5
Bicycle
0,4
Car
0,3
0,2
0,1
0,0
0
100000 200000 300000 400000 500000 600000
Time Step
Gulyás László
36
Challenge in Estimation

Endogeneity!
Gulyás László
37
Overview

On Agent-Based Modeling (ABM)



ABMs as Stochastic Processes



Properties, Praise & Critique
Example
Source of Randomness
Basic ABM Methodology
Verification & Validation


Challenges & Directions
Networks


Experimental Validation


Example
Example
Conclusions
Gulyás László
38
Verification & Validation

Directions II.
Experimental Validation
 Participatory Simulation

 The
case of the SFI-ASM
Gulyás László
39
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?
Gulyás László
40
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.
Gulyás László
41
Participants Learn
Fundamental Trading
Normalized Wealth

First
set of Experiments:
1.4
MinComp
1.2
initially applied technical
0.8 trading, but gradually discovered
1 Humans
0.6
fundamental strategies.
0.4
0.2

0
AvgComp
MaxComp
MinHuman
The winning human’s strategy was:
 Buy
1
if price < FV, sell otherwise.
AvgHuman
1001
Time period
Gulyás László
MaxHuman
42
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.
Gulyás László
43
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.
Gulyás László
44
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.
Gulyás László
45
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.
Gulyás László
46
Overview

On Agent-Based Modeling (ABM)



ABMs as Stochastic Processes



Properties, Praise & Critique
Example
Source of Randomness
Basic ABM Methodology
Verification & Validation


Challenges & Directions
Networks


Experimental Validation


Example
Example
Conclusions
Gulyás László
47
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.
Gulyás László
48