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Talk, but speak clearImproving the rigour in agent-based social simulation
Matteo RichiardiUniversità Politecnica delle Marche
and Collegio Carlo Alberto – LABORatorio R. Revelli
ESSA 2007,
September 10-15, 2007, Toulouse
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Outline
What is Agent-based Computational Economics (ACE)
Main features
When to use an agent-based model
The dual problem of micro-macro relation
A dynamic system representation of agent-based models
The notion of equilibrium in agent-based models
Analysis of the models
Estimation / calibration of the parameters
Description of the models
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References
• Leombruni, Richiardi, Saam, Sonnessa (2006), “A Common Protocol for Agent Based Social Simulation”, JASSS, 9(1)
• Richiardi, “Agent-based Computational Economics. A Short Introduction”, mimeo
• ….
downloadable from
www.dea.unian.it/richiardi/richiardi.htm
www.dea.unian.it/richiardi/courses/phd_ace.htm
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What is ACE
Agent-based computational models are models in which:
(i) a multitude of objects interact with each other and with the environment
(ii) the objects are autonomous, i.e. there is no central, or “top down” control over their behavior;
(iii) the outcome of their interaction is numerically computed.
“ACE is the computational study of economic processes modeled as dynamic systems of interacting agents.” (L. Tesfatsion)
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A methodological remark
Methodological individualism: explaining society as the aggregation of decisions by individuals (Austrian School of Economics). Reductionism: the whole is nothing but the sum of its parts.
ACE
Holism: the proprierties of a system cannot be deduced by the properties of its components alone. Indeed, the system as the whole determines how the parts behave: the whole is more than the sum of its parts (Aristotle, Metaphysics). Organicism (Ritter, 1919): the organization, not the composition, of organisms is what counts.
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Main features of ACE models
Heterogeneity
Explicit space
Local interaction
Cognitive foundations:
Bounded rationality
Limited / asymmetric information
Non equilibrium dynamics
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When to use ACE
To get a quick intuition of the dynamics a given system is
able to produce (scrap paper use)
To thoroughly investigate models that are not susceptible of a
more traditional analysis, or are susceptible of a more
traditional analysis only at too a high cost:
1. Numerical computation of analytical models
2. Robustness analysis of analytical models
3. Stand-alone simulation models
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When to use ACE
Analytical models: little interaction, little dynamics,
sophysticated behaviors (often, not always)
Simple behaviors can produce complex patterns
(e.g. Langton’s ants) [GO]
Simple choices can lead to complex and diversified behaviors
(e.g. El Farol bar problem, W. Brian Arthur, “Inductive
reasoning and bounded rationality”, American Economic
Review, n. 84, p. 406, 1994)
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The dual problem
The dual problem of the micro-macro relation:
a)FROM MICRO TO MACRO: Find the aggregate implications of given individual behaviors
b)FROM MACRO TO MICRO: Find the conditions at the micro level that give raise to some observed macro phenomena - ACE as generative social science: “If you didn’t grow it, you didn’t explain it” (Epstein, 1999)
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Our real problem
• a growing community of modellers
• a disappointing publication rate
• audience is more often interested in the methodology than in
the topic autoreferentiality
ABM papers seem to be confined only to specialized journals like
the Journal of Economic Dynamics and Control, the Journal
of Artificial Societies and Social Simulation, Computational
Economics, the Journal of Economic Interaction and
Coordination, Advances in Complex Systems and few others
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The real problem
How can
the rate of acceptance
of papers with agent-based methodology
in the top journals
be increased?
Talk to the mainstream !!!
Break the auto-referentiality circuit !!!
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Traditional analytical modelling
Traditional analytical modelling relies on a very well established,
although implicit, methodological protocol,
both with respect to:
• the way models are presented and to
• the kind of analyses that are performed.
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Traditional analytical modelling
E.g., in most papers:
• detailed reference to the literature;
• the model often adopts an existing framework and extends, or
departs from, well-known models only in limited respects;
• this allows a concise description, and saves more space for the
results, which are
• finally confronted with empirical data;
• when estimation is involved measures of validity and
reliability of the estimates are always presented, in a
• very standardized way.
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Agent based modelling
E.g., in most papers:
• very limited reference to the literature;
• the model often departs radically from the existing literature
and adopts or extends no existing, well-known framework.
• This allows only a superficial description of the model, and
even leaves no space for the results, which are
• only rarely confronted with empirical data.
• When estimation is involved few measures of validity and
reliability of the estimates are presented, often in a
• very unstandardized way.
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ACE is mathematics
Computer simulation as a third symbol system, aside verbal description and mathematics (Ostrom, 1988)
“Simulation is neither good nor bad mathematics, but no mathematics at all” (Gilbert et al., 1999)
“Any theory that can be expressed in either of the first two symbol systems can also be expressed in the third symbol system.”
“There might be verbal theories which cannot be adequately expressed in the second symbol system of mathematics, but can be in the third”
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ACE models as recursive systems
behavioral rules
state variables
structural parameters
);,( ,,1,1, tittiiti xxfx
);,( ,,1,1, tittiiti xxa
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),...,;,...,(
)),,(),...,,,((
),...,(
0,0,10,0,1
1,1,1,1,11,11,11
,,1
nnt
tntntnnttt
tntt
xxg
xxfxxfs
xxsY
I-O transformation function
initial conditions
ACE models as recursive systems
structural parameters
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2 notions of equilibrium: AT A MICRO LEVEL, when individual strategies are
constant
AT A MACRO LEVEL, when some relevant aggregate statistics of the system are stationary:
Equilibrium
),...,;,...,(lim 0,0,10,0, nnitt
e xxa
),...,;,...,(lim 0,0,10,0, nnitt
e xxgYY
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g is unknown get an inductive evidence about g, by performing multiple
(thousands, millions) runs and recording inputs and outputs of each run
Interpretation of results
),...,;,...,(lim 0,0,10,0, nnitt
e xxgYY
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sensitivity analysis around some default values of the parameters and initial conditions: keep all parameters and initial conditions fixed and change only one at a time
Local analysis of g
equivalent to exploring the partial derivatives of g
choice of the default values is an issue
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Let all parameters change between the different simulation runs
Get an estimate of g
(metamodel, response surface, compact model, emulator, ecc.)
Global analysis of g
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“the distinction drawn between calibrating and estimating the parameters of a model is artificial at best. Moreover, the justification for what is called “calibration” is vague and confusing. In a profession that is already too segmented, the construction of such artificial distinctions is counterproductive” (Hansen and Heckman, 1996)
Choice of structural parameters: some parameters have real counterparts and their value is
known: no need for calibration/estimation otherwise: choice of the values that make the artificial data
produced via simulation as close as possible to the real data
Calibration / estimation
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Gouriereux and Monfort, 1997 Mariano et al, 2000 Train, 2003
define some target variables (e.g. moments) compute them both in the artificial and in the real data keep changing the parameters to estimate (the ) until the
distance between the values of the target variables in the artificial data and in the real data is minimized
Indirect Inference: the targets are the estimates of an auxiliary model
Simulation based estimation
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code availability the sequence of events in the simulation must be carefully
described:
pseudocode time-sequence diagrams
Replicability
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The pseudo-code
…
Source: Neugart (2006)
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Time-sequence diagrams
Source: Richiardi (2007)
