http://www.pnas.org/content/99/suppl.3/7280.full
Agent-based modeling: Methods and techniques for simulating human systems
Abstract
Agent-based modeling is a
powerful simulation modeling technique that has seen a number of
applications in the last few years,
including applications to real-world
business problems. After the basic principles of agent-based simulation
are briefly introduced,
its four areas of application are
discussed by using real-world applications: flow simulation,
organizational simulation,
market simulation, and diffusion
simulation. For each category, one or several business applications are
described and analyzed.
In agent-based modeling (ABM), a
system is modeled as a collection of autonomous decision-making
entities called agents.
Each agent individually assesses its
situation and makes decisions on the basis of a set of rules. Agents
may execute various
behaviors appropriate for the system they
represent—for example, producing, consuming, or selling. Repetitive
competitive
interactions between agents are a feature of
agent-based modeling, which relies on the power of computers to explore
dynamics
out of the reach of pure mathematical methods
(1, 2). At the simplest level, an agent-based model consists of a system of agents and the relationships between them. Even a
simple agent-based model can exhibit complex behavior patterns (3)
and provide valuable information about the dynamics of the real-world
system that it emulates. In addition, agents may
be capable of evolving, allowing
unanticipated behaviors to emerge. Sophisticated ABM sometimes
incorporates neural networks,
evolutionary algorithms, or other learning
techniques to allow realistic learning and adaptation.
ABM is a mindset more than a
technology. The ABM mindset consists of describing a system from the
perspective of its constituent
units. A number of researchers think that
the alternative to ABM is traditional differential equation modeling;
this is
wrong, as a set of differential equations,
each describing the dynamics of one of the system's constituent units,
is an
agent-based model. A synonym of ABM would be
microscopic modeling, and an alternative would be macroscopic modeling.
As
the ABM mindset is starting to enjoy
significant popularity, it is a good time to redefine why it is useful
and when ABM
should be used. These are the questions this
paper addresses, first by reviewing and classifying the benefits of
ABM and
then by providing a variety of examples in
which the benefits will be clearly described. What the reader will be
able to
take home is a clear view of when and how to
use ABM. One of the reasons underlying ABM's popularity is its ease of
implementation:
indeed, once one has heard about ABM, it is
easy to program an agent-based model. Because the technique is easy to
use, one
may wrongly think the concepts are easy to
master. But although ABM is technically simple, it is also conceptually
deep.
This unusual combination often leads to
improper use of ABM.
Benefits of Agent-Based Modeling.
The benefits of ABM over other modeling techniques can be captured in three statements: (i) ABM captures emergent phenomena; (ii) ABM provides a natural description of a system; and (iii) ABM is flexible. It is clear, however, that the ability of ABM to deal with emergent phenomena is what drives the other
benefits.
ABM captures emergent phenomena.
Emergent
phenomena result from the interactions of individual entities. By
definition, they cannot be reduced to the system's
parts: the whole is more than the sum of
its parts because of the interactions between the parts. An emergent
phenomenon
can have properties that are decoupled
from the properties of the part. For example, a traffic jam, which
results from the
behavior of and interactions between
individual vehicle drivers, may be moving in the direction opposite
that of the cars
that cause it. This characteristic of
emergent phenomena makes them difficult to understand and predict:
emergent phenomena
can be counterintuitive. Numerous
examples of counterintuitive emergent phenomena will be described in
the following sections.
ABM is, by its very nature, the canonical
approach to modeling emergent phenomena: in ABM, one models and
simulates the
behavior of the system's constituent
units (the agents) and their interactions, capturing emergence from the
bottom up when
the simulation is run.
Here is a simple example of an
emergent phenomenon involving humans. It is a game that is easy to play
with a group of 10–40
people. One asks each member of the
audience to randomly select two individuals, person A and person B. One
then asks them
to move so they always keep A between
them and B so A is their protector from B. Everyone in the room will
mill about in
a seemingly random fashion and will soon
begin to ask why they are doing this. One then asks them to move so
that they keep
themselves in between A and B (they are
the Protector). The results are striking: almost instantaneously the
whole room
will implode, with everyone clustering in a
tight knot. This example shows how simple individual rules can lead to
coherent
group behavior, how small changes in
those rules can have a dramatic impact on the group behavior, and how
intuition can
be a very poor guide to outcomes beyond a
very limited level of complexity. The group's collective behavior is
an emergent
phenomenon. By using a simple agent-based
simulation (available at www.icosystem.com/game.htm)
in which each person is modeled as an autonomous agent following the
rules, one can actually predict the emerging collective
behavior. Although this is a simple
example, where individual behavior does not change over time, ABM
enables one to deal
with more complex individual behavior,
including learning and adaptation.
One may want to use ABM when there is potential for emergent phenomena, i.e., when: -
Individual behavior is nonlinear and can be characterized by thresholds, if-then rules, or nonlinear coupling. Describing discontinuity in individual behavior is difficult with differential equations.
-
Individual behavior exhibits memory, path-dependence, and hysteresis, non-markovian behavior, or temporal correlations, including learning and adaptation.
-
Agent interactions are heterogeneous and can generate network effects. Aggregate flow equations usually assume global homogeneous mixing, but the topology of the interaction network can lead to significant deviations from predicted aggregate behavior.
-
Averages will not work. Aggregate differential equations tend to smooth out fluctuations, not ABM, which is important because under certain conditions, fluctuations can be amplified: the system is linearly stable but unstable to larger perturbations.
Interestingly, because ABM
generates emergent phenomena from the bottom up, it raises the issue of
what constitutes an explanation
of such a phenomenon. The broader agenda
of the ABM community is to advocate a new way of approaching social
phenomena, not
from a traditional modeling perspective
but from the perspective of redefining the scientific process entirely.
According
to Epstein and Axtell (1),
“[ABM] may change the way we think about explanation in the social
sciences. What constitutes an explanation of an observed
social phenomenon? Perhaps one day people
will interpret the question, ‘Can you explain it?’ as asking ‘Can you
grow it?’.”
ABM provides a natural description of a system.
In many
cases, ABM is most natural for describing and simulating a system
composed of “behavioral” entities. Whether one
is attempting to describe a traffic jam,
the stock market, voters, or how an organization works, ABM makes the
model seem
closer to reality. For example, it is
more natural to describe how shoppers move in a supermarket than to
come up with the
equations that govern the dynamics of the
density of shoppers. Because the density equations result from the
behavior of
shoppers, the ABM approach will also
enable the user to study aggregate properties. ABM also makes it
possible to realize
the full potential of the data a company
may have about its customers: panel data and customer surveys provide
information
about what real people actually do.
Knowing the actual shopping basket of a customer makes it possible to
create a virtual
agent with that shopping basket rather
than a density of people with a synthetic shopping basket computed from
averaging
over shopping data.
The difference between business
processes and activities provides another example of how much more
natural ABM is. A business
process is an abstraction, sometimes
useful, which is often difficult for people inside an organization to
relate to. ABM
looks at the organization from the
viewpoint not of business processes but of activities, that is, what
people inside the
organization actually do (Fig. 1).
Fig. 1.
Illustration of the business process and agent views of a business.
The two descriptions must, of
course, be mutually consistent. The business process description
actually provides the modeler
with a useful consistency check. However,
when it comes to populating, validating, and calibrating the model,
people inside
the organization have an easier time
answering questions about their own activities: they can relate to the
model because
the models describes their activities.
One may want to use ABM when describing the system from the perspective of its constituent units' activities is more natural,
i.e., when:
-
The behavior of individuals cannot be clearly defined through aggregate transition rates.
-
Individual behavior is complex. Everything can be done with equations, in principle, but the complexity of differential equations increases exponentially as the complexity of behavior increases. Describing complex individual behavior with equations becomes intractable.
-
Activities are a more natural way of describing the system than processes.
-
Validation and calibration of the model through expert judgment is crucial. ABM is often the most appropriate way of describing what is actually happening in the real world, and the experts can easily “connect” to the model and have a feeling of “ownership.”
-
Stochasticity applies to the agents' behavior. With ABM, sources of randomness are applied to the right places as opposed to a noise term added more or less arbitrarily to an aggregate equation.
ABM is flexible.
The
flexibility of ABM can be observed along multiple dimensions. For
example, it is easy to add more agents to an agent-based
model. ABM also provides a natural
framework for tuning the complexity of the agents: behavior, degree of
rationality, ability
to learn and evolve, and rules of
interactions. Another dimension of flexibility is the ability to change
levels of description
and aggregation: one can easily play
with aggregate agents, subgroups of agents, and single agents, with
different levels
of description coexisting in a given
model. One may want to use ABM when the appropriate level of
description or complexity
is not known ahead of time and finding
it requires some tinkering.
Areas of Application.
Examples of emergent phenomena abound in the social, political, and economic sciences. It has become progressively accepted that some phenomena can be difficult to predict and even counterintuitive. In a business context, situations of interest where emergent phenomena may arise can be classified into four areas:-
Flows: evacuation, traffic, and customer flow management.
-
Markets: stock market, shopbots and software agents, and strategic simulation.
-
Organizations: operational risk and organizational design.
-
Diffusion: diffusion of innovation and adoption dynamics.
The rest of the article is organized around these areas of application.
Flows
Evacuation.
Crowd
stampedes induced by panic often lead to fatalities as people are
crushed or trampled. Such phenomena may be triggered
in life-threatening situations such as
fires in crowded buildings or may arise from the rush for seats or
sometimes seemingly
without causes. Recent examples include
the panics in Harare, Zimbabwe, and at the Roskilde rock concert in
Denmark. The
frequency of such disasters seems to be
increasing as growing population densities combined with easier
transportation lead
to greater mass events such as pop
concerts, sporting events, and demonstrations. Panicking people are
obsessed by short-term
personal interests uncontrolled by social
and cultural constraints. The reduced attention in situations of fear
also causes
such alternatives as side exits to be
mostly ignored. In addition, there is social contagion, that is, a
transition from
individual to mass psychology, in which
individuals transfer control over their actions to others, leading to
conformity.
Such irrational herding behavior often
leads to bad overall results such as dangerous overcrowding and slower
escape, increasing
the fatalities or, more generally, the
damage. In agent terms, collective panic behavior is an emergent
phenomenon that
results from relatively complex
individual-level behavior and interactions between individuals
(hypnotic effect, mutual
excitation of a primordial instinct,
circular reactions, and social facilitation). ABM seems ideally suited
to provide valuable
insights into the mechanisms of and
preconditions for panic and jamming by in-coordination. Simulation
results (4, 5)
suggest practical ways of minimizing the harmful consequences of such
events and the existence of an optimal escape strategy.
For example, let us consider a fire
escape situation in a confined space: a movie theatre or a concert
hall. Let us assume
that there is one exit available. How can
one increase the outflow of people? Narrowing down the problem, one
could ask:
what is the effect of putting a column (a
pillar) just before exit, slightly asymmetrically (for example, to the
left of
the exit), about 1 m away from the exit?
Intuitively, one might think the column will slow down the outflow of
people. However,
ABM, backed by real-world experiments,
indicates that the column regulates the flow, leading to fewer injured
people and
a significant increase in the flow,
especially if one assumes that injured people cannot move and impede
the flow (4). This result is an example of a counterintuitive consequence of an emergent phenomena: who would think of putting a column
in front of an emergency exit? ABM captures that emergent phenomenon in a natural way (Fig. 2).
Fig. 2.
Fire escape agent-based simulation (live simulation available at www.helbing.org). People are represented by circles, green circles being injured people. Simulations assume 200 people in a room. (a) No column. (b) With column, after 10 s. (c) With column, after 20 s. In the absence of the column, 44 people escape and 5 are injured after 45 s; with the column, 72
people escape and no one is injured after 45 s. After Helbing et al. (4).
Flow Management.
An obvious flow management application of ABM is traffic. One of the most ambitious modeling projects in this area has been
under way at the Los Alamos National Laboratory (LANL) for several years (transims.tsasa.lanl.gov).
A team from LANL's Technology and Safety Assessment Division has
developed a traffic simulation software package to create
products that can be deployed to
metropolitan planning agencies nationwide. The TRansportation ANalysis
SIMulation System
(TRANSIMS) ABM package provides planners
with a synthetic population's daily activity patterns (such as travel
to work, shop,
and recreation, etc.), simulates the
movements of individual vehicles on a regional transportation network,
and estimates
air pollution emissions generated by
vehicle movements. Travel information is derived from actual census and
survey data
for specific tracts in target cities,
providing a more accurate sense of the movements and daily routines of
real people
as they negotiate a full day with various
transportation options available to them. TRANSIMS is based on (and
contributes
to the further development of) advanced
computer simulation codes developed by Lawrence Livermore National
Laboratory for
military applications. TRANSIMS models
create a virtual metropolitan region with a complete representation of
the region's
individuals, their activities, and the
transportation infrastructure. Trips are planned to satisfy the
individuals' activity
patterns. TRANSIMS then simulates the
movement of individuals across the transportation network, including
their use of
vehicles such as cars or buses, on a
second-by-second basis. This virtual world of travelers mimics the
traveling and driving
behavior of real people in the region. The
interactions of individual vehicles produce realistic traffic dynamics
from which
analysts using TRANSIMS can estimate
vehicle emissions and judge the overall performance of the
transportation system. Previous
transportation planning surveyed people
about elements of their trips such as origins, destinations, routes,
timing, and
forms of transportation used, or modes.
TRANSIMS starts with data about people's activities and the trips they
take to carry
out those activities, then builds a model
of household and activity demand. The model forecasts how changes in
transportation
policy or infrastructure might affect
those activities and trips. TRANSIMS tries to capture every important
interaction
between travel subsystems, such as an
individual's activity plans and congestion on the transportation
system. For instance,
when a trip takes too long, people find
other routes, change from car to bus or vice versa, leave at
different times, or decide not to engage in a certain activity at a
given location. Also, because TRANSIMS tracks
individual travelers—locations, routes,
modes taken, and how well their travel plans are executed—it can
evaluate transportation
alternatives and reliability to determine
who might benefit and who might be adversely affected by
transportation changes.
In the initial case studies, a
25-square-mile portion of the Dallas/Fort Worth region was used for
demonstrating the first
TRANSIMS version. Using existing
Dallas/Fort Worth production/attraction zonal data, activities, and
plans for ≈3.5 million
travelers were generated for the hours of
5:00–10:00 a.m. Of these plans, those falling within a 25-square-mile
study region
were used as input to the simulation
module to compare two infrastructure changes with respect to how each
helped alleviate
congestion. Although both alternatives
improved congested conditions and flow along the freeway, an unexpected
result was
that the alternative of improving local
arterials was superior to the alternative of adding lanes to the
freeway from the
perspective of network reliability.
Network reliability is a measure of day-to-day variability in travel
times experienced
by travelers. In other words, if it takes
one anywhere from 10 to 30 min to drive to work, network reliability
is low; if
it takes one between 10 and 12 min,
network reliability is high. The team has recently been simulating the
metropolitan
region of Portland, OR, a model that
requires 120,000 links and 1.5 million travelers, an order of magnitude
larger than
the Dallas/Fort Worth simulation of
10,000 links and 200,000 travelers. The benefits of the ABM approach
are obvious: better
and more efficient infrastructure
planning, including not only better throughput but also compliance in
terms of emissions,
enabled by the ability of ABM to capture
and reproduce emergent traffic phenomena.
Another application of ABM to flow
management is the simulation of customer behavior in a theme park or
supermarket. The
collective patterns generated by
thousands of customers can be extremely complex as customers interact:
for example, how
long one waits at an attraction in a
theme park depends on other people's choices. A major theme park resort
company was
thinking about how to improve adaptability
in labor scheduling, but knew that this depended on knowing more about
the optimal
balance of capacity and demand. Axtell and
Epstein developed ResortScape (13), an agent-based model of the park that provides an integrated picture of the environment and all of the interacting elements
that come into play in such a resort. The model provides a fast in silico way for managers to identify, adjust, and watch the impact of any number of management levers such as:
-
When or whether to turn off a particular ride.
-
How to distribute rides per capita throughout the park space.
-
What is the tolerance level for wait times.
-
When to extend operating hours.
In the simulation, agents
represent a realistic and changeable mix of both supply (attractions,
shops, food concessions)
and demand (visitors with different
preferences) elements of a day at the park. Leveraging existing
resources and data,
such as customer surveys, segmentation
studies, queue timers, people counters, attendance estimates, and
capacity figures,
the model generates information about
guest flow. Users can design and run an infinite number of scenarios to
study the
dynamics of the park space, test the
effectiveness of various management decisions, and track visitor
satisfaction throughout
the day.
ABM is particularly useful in
this context, because the mapping between the agents' preferences and
behaviors on the one
hand, and the park's performance (in
terms of average waiting times, number of attractions visited, total
distance walked,
etc.) on the other is too complex to be
dealt with by using mathematical techniques and purely statistical
analysis of the
data. Why is the mapping too complex?
Because, for example, the time a given customer has to wait at a given
attraction
depends on what other customers are doing,
how they respond to different park conditions, what their wish list
is, etc. The
flow of customers in the park and the
money they spend are “emergent” properties of interactions among and
between customers
and the spatial layout of the park.
Therefore, simulating the park's operations with a given layout seems
to be the only
solution. ABM is the most natural and
easiest way of describing the system, because the actors of this system
are customers
(and attractions) with a behavior of their
own. For example, waiting times at a theme park attraction result from
the interactions
of many behavioral units: the customers.
Finally, the data available to the modeler are naturally structured for
ABM: the
available data are a description of the
desires and behaviors of a number of customers.
Along the same lines, Bilge, Venables, and Casti have developed an agent-based model of a supermarket (www.simworld.co.uk) (6). SimStore is a model of a real British supermarket, the Sainsbury's store at South Ruislip in West London. The agents in SimStore
are software shoppers armed with shopping lists. They make their way
around the silicon store, picking goods off the shelves
according to rules such as the
nearest-neighbor principle: “Wherever you are now, go to the location
of the nearest item
on your shopping list.” Using these
rules, SimStore generates the paths taken by customers, from which it can calculate customer densities at each location.
It is also possible to link all
points visited by, say, at least 30% of customers to form a most
popular path. An optimization
algorithm can then change where in the
supermarket different goods are stacked and so minimize, or maximize,
the length
of the average shopping path. Shoppers,
of course, do not want to waste time, so they want the shortest path.
But the store
manager would like to have them pass by
almost every shelf to encourage impulse buying. So there is a dynamic
tension between
the minimal and maximal shopping paths.
This model was originally aimed at helping Sainsbury's to redesign its
stores to
generate greater customer throughput,
reduce inventories, and shorten the time that products are on the
shelves.
Macy's is a department store chain using ABM (7).
In 1997, Macy's East approached PricewaterhouseCoopers with the
following question: “How do we know when we have the
right number of salespeople on the
selling floor?” According to industry veterans, the retail business is a
business of
averages, where analysis is done on a
spreadsheet. It is a business that deals with sales volume per hour as
the determining
factor in its allocation of salespeople,
and the number of salespeople placed on the selling floor is based on
the velocity
in sales predicted for a specific day. And
yet real behavior is the result of interactions between individuals,
not averages.
With ABM, Macy's had the opportunity to
use visualization to review data in a way that becomes informational
and leads to
solutions. Spreadsheet data averages can
be used to estimate distributions of individual behavior, so the
individual agents
in the simulation are consistent with the
available real-world data. But because the agents represent
individuals, the actual
flow of their behavior can be much more
realistic and informative. So instead of making estimates from the top
down, Macy's
can observe how volume really occurs from
the bottom up. The virtual store can be modified in terms of layout
(shelves, cash
register positions, gates, etc.) and
number of employees per department to see how these changes influence
the affective
state of a large number of agents. One
can then explore the space of levers to maximize the number of happy
customers in
the most cost-effective way. Results from
the model include the observation of “microbursts” of demand, where
customers
may be doing “project shopping” (e.g.,
buying an outfit and then accessorizing it), the importance of
proximity to items
(physical placement as well as
brand-relatedness), which helps drive impulse buying.
Markets
The dynamics of the stock market
results from the behavior of many interacting agents, leading to
emergent phenomena that
are best understood by using a bottom-up
approach—ABM. There has been an upsurge of interest in agent-based
models of markets
in the last few years, stimulated by the
pioneering work of Arthur and colleagues (8, 9). One commercial application has been developed by Bios Group for the National Association of Security Dealers Automated
Quotation (NASDAQ) Stock Market (www.cbi.cgey.com/journal/issue4/features/future/future.pdf).
In 1997, the NASDAQ Stock Market was about to implement a sequence of
apparently small changes: reduction in tick size,
from 1/8th to 1/16th and so on down to
pennies. NASDAQ considers changes in trading policies very carefully:
NASDAQ stands
to lose a great deal if a new rule
provokes a negative network-wide response from investors, market
makers, and issuers.
In the past, NASDAQ executives have
analyzed the financial marketplace through economic studies, financial
models, and feedback
from market participants. The Market
Quality Committee establishes regulations largely as a result of input
from economists,
lawyers, lobbyists, and policy makers.
To evaluate the impact of
tick-size reduction, NASDAQ has been using an agent-based model that
simulates the impact of regulatory
changes on the financial market under
various conditions. The model allows regulators to test and predict the
effects of
different strategies, observe the
behavior of agents in response to changes, and monitor developments,
providing advance
warning of unintended consequences of
newly implemented regulations faster than real time and without risking
early tests
in the real marketplace. In the
agent-based NASDAQ model, market maker and investor agents
(institutional investors, pension
funds, day traders, and casual investors)
buy and sell shares by using various strategies. The agents' access to
price and
volume information approximates that in
the real-world market, and their behaviors range from very simple to
complicated
learning strategies. Neural networks,
reinforcement learning, and other artificial intelligence techniques
were used to
generate strategies for agents. This
creative element is important because NASDAQ regulators are especially
interested in
strategies that have not yet been
discovered by players in the real market, again to approach their goal
of designing a
regulatory structure with as few loopholes
as possible, to prevent abuses by devious players.
The model produced some
unexpected results. Specifically, the simulation suggests a reduction
in the market's tick size can
reduce the market's ability to perform
price discovery, leading to an increase in the bid–ask spread. A spread
increase
in response to tick-size reduction is
counterintuitive because tick size is the lower bound on the spread.
Initially, it
was believed that the implementation of
decimalization would be conducive to tighter spread, easing the
discrepancy between
bids and asking prices. Decimalization,
overall, was thought to be highly efficient and effective. Among market
professionals,
the perceived wisdom is that providing
greater granularity of price denomination is good for investors because
it promotes
competition among buyers and sellers who
can negotiate in more precise terms, and thus it drives the market's
spread down,
which results in better prices for
investors. This wisdom is difficult to test empirically: the complexity
of market behavior
makes isolating cause and effect highly
problematic. Without a computer simulation, rule makers are stuck with
an intuitive
argument, and one that is poor in detail,
judging market interaction by only one measure: competition (and hence
price).
Other dimensions of the problem go
unaddressed: if better prices are available, do only small investors
benefit, or will
large ones benefit too? Will smaller tick
sizes make the market more jittery and volatile?
A spreadsheet model or even system dynamics (10)
(a popular business-modeling technique that uses sets of differential
equations) would not have been able to generate
the same deep insights as ABM, because
the behavior of the market emerges out of the interactions of the
players, who in
turn may change their behavior in response
to changes in the market. The interactions between investors, market
makers,
and the operating rules of the NASDAQ
Stock Market make the entire system's dynamics quite hard to
understand. Predicting
how it would change under a new set of
operating regulations cannot be based on intuition or on classical
modeling techniques,
because they are not suited to describe
the complexities of the behavior of the stock market agents. For
example, the mapping
between tick size and spread can be
understood only by taking into account details of the investors' and
market makers'
behavior to model the process of price
discovery.
Stock markets are not the only
markets that can be better understood by using ABM. For example,
auctions can benefit from
the approach. Indeed, electronic double
auctions using intelligent agents have many applications today. eBay
uses intelligent
agents to allow customers to automate the
bidding process, but these could be made much more sophisticated by
using ABM
to test a variety of robot behaviors.
Designing intelligent agents that have desired aggregate properties
could turn out
to be the “killer app” that will make the
cyber world the preferred medium for economic transactions. Shopbots
are Internet
agents that automatically search for
information that pertains to the price and quality of goods and
services. As the prevalence
of shopbots in electronic commerce
increases, the resultant reduction in economic friction because of
decreased search costs
could dramatically alter market behavior.
Some predict that intelligent agents eventually will transform our
world, which
means they may trade information, gather
information, translate information, and perform all sorts of
negotiations for us
in the future. Ultimately, transactions
among economic software agents will constitute an essential and perhaps
even dominant
portion of the world economy. It is
tempting to assume that the same mechanisms can be applied successfully
to software agents.
But one must be very careful about the
introduction of agent technology, as agents behave in a way that is
still poorly
understood. For example, in an all-agent
auction, prices tend to rise, reach a peak, and then suddenly dip
dramatically
before the same process begins again.
IBM's Kephart and his colleagues have been exploring the potential
impact of shopbots
on market dynamics, by simulating and
analyzing an agent-based model of shopbot economics, which incorporates
software agent
representations of buyers and sellers (11).
Their model is similar to some that are studied by economists
interested, for example, in the phenomenon of price dispersion,
with different underlying assumptions and
methodology: here the goal is to design economic software agents, rather than “just” explain human economic behavior. In particular, they have been examining agent
economies in which (i) search costs are nonlinear; (ii) some portion of the buyer population makes no use of search mechanisms; and (iii)
shopbots are economically motivated, strategically pricing their
information services so as to maximize their own profits.
Under these conditions, they have found
that markets can exhibit a variety of hitherto unobserved dynamical
behaviors, including
complex limit cycles and the coexistence
of multiple buyer search strategies. A shopbot that charges buyers for
price information
can manipulate markets to its own
advantage, sometimes inadvertently benefiting buyers and sellers.
The same ABM techniques that are
used to study the stock market or the collective behavior of shopbots
can be applied to
situations where there are many agents
playing economic games. That is “game theory without the theory.” Game
theory is
a great framework, but game theorists
suffer from self-imposed constraints: being able to prove theorems puts
severe limitations
to what is possible. In particular, any
realistic situation is likely to lie beyond the grasp of theory.
Axelrod (2) argues that agent-based game theory is the only way forward.
A team at Icosystem Corporation has simulated the Internet service provider (ISP) market with ABM (www.icosystem.com).
The agents are used to represent both the ISPs and their customers.
Each ISP is an agent and each customer is an agent.
The ISPs' offerings are confronted with
customers' needs and expectations; customers make decisions (to adopt,
leave, or
switch) depending on the match between
their profiles and the ISPs'. One of the attributes of the ISPs, among
may others,
is how much they charge monthly for their
services. ISPs that do not make enough money are eliminated following
an “evolutionary”
dynamics; those that are successful give
rise to copycats (that is, ISPs with similar business models) and also
fine tune
their own business models. ABM produced
two significant results: (i) It discovered the free ISP business model (no monthly fee). (ii)
It predicted the instability of the free ISP business model: the first
free ISP that emerges in the simulation differentiates
itself from the pack by providing
services without charging monthly fees and making money on advertising.
These two properties
emerge out of the interaction dynamics
between the ISPs through the marketplace. Because ISPs learn and
evolve, it would
have been difficult to obtain this insight
by using other simulation methods.
Organizations
One promising area of application for ABM is organizational simulation (12).
It is clearly possible to model the emergent collective behavior of an
organization or of a part of an organization in
a certain context or at a certain level of
description. At the very least, the process of designing the
simulation produces
valuable qualitative insights. But, in
certain cases, one is also able to generate semiquantitative insights. A
good illustration
of this is an agent-based model of
operational risk (www.businessinnovation.ey.com/events/pubconf/2000–04-28/ec5transcripts/BonabeauNivollet.pdf) (13).
A human organization is often
subject to operational risk. Consider financial institutions.
Operational risk arises from
the potential that inadequate information
systems, operational problems, breaches in internal controls, fraud,
or unforeseen
catastrophes will result in unexpected
losses. According to the Basle Committee on Banking, operational risk
involves breakdowns
in internal controls and corporate
governance that can lead to financial losses through error, fraud, or
failure to perform
in a timely manner or cause the interests
of the bank to be compromised in some other way, for example, by its
dealers,
lending officers, or other staff exceeding
their authority or conducting business in an unethical or risky
manner. It is
increasingly viewed as the most important
risk that banks face. Examples of large operational losses include
Daiwa, Sumitomo,
Barings, Salomon, Kidder Peabody, Orange
County, Jardine Fleming, and more recently NatWest Markets, the Common
Fund, or
Yamaichi. Although most banks have
developed efficient and sometimes sophisticated ways of dealing with
market risk and
to large extent credit risk, they are
still in the early stages of developing operational risk measurement
and monitoring.
Unlike market and credit risk, operational
risk factors are largely internal to the organization, and a clear
mathematical
or statistical link between individual
risk factors and the size and frequency of operational loss does not
exist. Experience
with large losses is infrequent, and many
banks lack a time series of historical data on their own operational
losses and
their causes. Uncertainty about which
factors are important arises from the absence of a direct relationship
between the
risk factors usually identified (measured
through internal audit ratings, internal control self-assessment based
on such
indicators as volume, turnover, error
rates, and income volatility) and the size and frequency of loss
events. This contrasts
with market risk, where changes in prices
have an easily computed impact on the value of the bank's trading
portfolio, and
with credit risk, where changes in the
borrower's credit quality are often associated with changes in the
interest rate
spread of the borrower's obligations over a
risk-free rate. Given all of the characteristics of operational risk,
it is
obviously difficult to quantify.
Operational historical data are so scarce that it is not possible to
allocate capital reliably
and efficiently, and it is not possible
to obtain good VAR (value-at-risk) and RAROC (risk-adjusted return on
capital) estimates.
Capital allocation is important because
it gives managers an incentive to keep operational risk under control.
Yet there
is increasing pressure on financial
institutions to quantify operational risk in a way that convinces both
investors (efficient
allocation of capital) and regulatory
entities (risk under “control”). More precisely, a financial
institution must be able
to quantify operational risk within a
reliable framework to be able to keep risk under control, optimize
economic capital
allocation, and determine its insurance
needs.
Given the characteristics of
operational risk, bottom-up enterprise-wide simulation looks like a
promising approach (to
low-frequency high-impact operational
risk). What is needed is a framework that includes the possibility of
nonlinear effects
because of interactions among subunits
and to cascading events. The framework should be able to operate with
scarce data.
Hence the idea to simulate operations
from the bottom up to generate a large artificial data set that
includes large events.
The artificially generated data can then
be used to apply classical capital allocation techniques. Bios and Cap
Gemini Ernst
& Young (13)
have applied ABM techniques to measuring and managing operational risk
at Société Générale Asset Management (SGAM). A
simulation model of the business unit's
activities was designed, starting with business process modeling and
workflow identification.
By using the business process model and
the workflows the bank's “agents” were then identified, and their
activities were
modeled as well as their interactions with
other agents and the risk factors that could impact their activities.
To make
the tool tractable in the end the
activities had to be modeled in enough detail to capture the “physics”
of the bank but
not too much detail. The risk factors
were connected to the bank's profit and loss through potentially
complex pathways
in the organization, for example from a
client's order to the detection of a trading error in the back office.
Then the
bank's environment was modeled—the
markets, customers, regulators, etc. By running the model, it is
possible to generate
artificial earnings distributions, used to
estimate potential losses and their likelihood. For example, the bank
can compute
its “earnings-at-risk,” that is, the
minimum earnings that could be observed in one year at the bank with a
95% level of
confidence. The benefit to the bank: its
allocation of economic capital is backed by a simulation of how the
organization
operates rather than based on some
strange combination of industry-wide historical data and accounting
magic. If the model
is good, regulators accept it more easily
and the bank does not have to put aside 10 times the amount of economic
capital
it really needs. For an asset management
business, economic capital is a fraction of assets under management.
Reducing the
fraction by just 0.01% means millions of
dollars. Measuring is just the first step, though. An added benefit of
simulation
is that one can identify where losses
come from and test mitigation procedures.
When deciding to model a bank by
using ABM, one is not making an arbitrary modeling decision. One is
modeling the bank in
a way that is natural to the
practitioners, because one is modeling the activities of the bank by
looking at what every
actor does. If one is modeling the bank's
processes instead, it is more difficult for people to understand the
model because
one person's activities span many
processes. That has important consequences when it comes to populating,
validating, and
calibrating the model. If people “connect”
to the simulation model, in the sense that they recognize and
understand what
the model is doing, they can improve it,
more easily quantify what needs to be quantified, etc. Because they
have a deep
understanding of the risk drivers related
to their own activity, it is easier to incorporate the relevant risk
drivers into
the model. Once they have their
activities and the corresponding risk drivers in the model, they can
suggest control and
mitigation procedures and test them by
using the simulation tool. In other words, ABM is not only a simulation
tool; it
is a naturally structured repository for
self-assessment and ideas for redesigning the organization.
ABM is perfect not just for
operational risk in financial institution but for modeling risk in
general. Modeling risk in
an organization using ABM is THE right
approach to modeling risk because most often risk is a property of the
actors in
the organization: risk events impact
people's activities, not processes. For example, it is more natural to
say that someone
in accounting made a mistake (sent the
wrong invoice to a customer) than to say the receivables process was
impacted by
an error event in the invoicing
subprocess. ABM will revolutionize business risk advisory services
because it constitutes
a paradigm shift from spreadsheet-based
and process-oriented models. Populating, validating, and calibrating an
agent-based
model of risk is an order of magnitude
easier and makes much more sense than other models. The agent-based
model also makes
the formulation of mitigation strategies
easier. Within 3–6 years, ABM should be used routinely in audit.
What the Société Générale Asset Management example has hinted at is the idea of using ABM to design better organizations
(12).
Indeed, once one has a reliable model of an organization, it is
possible to play with it, change some of the organizational
parameters, and measure how the
performance of the organization varies in response to these changes.
Performance measurements
can range from how fast information
propagates in the organization to how good the organization is at
collectively performing
its task—inventing new products, selling,
or managing receivables.
Diffusion
In the context of this section,
ABM applies to cases where people are influenced by their social
context, that is, what others
around them do. Although a lot of academic
attention has been given to the subject, there are very few business
applications,
perhaps because of the “soft” nature of
the variables and the difficulty in measuring parameters. Social
simulation in business
has not been very successful so far,
because the emphasis has been on using it as a predictive tool rather
than as a learning
tool. For example, a manager can
understand her marketplace better by playing with an agent-based model
of it. Then, of
course, quantifying the tangible benefits
of something intangible is difficult, and a manager cannot claim to
have saved
$X million by playing with a
simulation of her customers. Still, there is a lot of value in using
social simulation in a business
context. Farrell and his team developed a
synthetic world populated by virtual agents to try to predict how (and
when) hits
happen (7). Working for Twentieth Century Fox, they modeled how such movies as “Titanic” or “The Blair Witch Project” could become
hits, but their model was not very successful. Predicting hits might be the single most difficult thing to do; understanding how hits happen is a better use of the model.
Let us examine a simple product
adoption model to illustrate the value of ABM in modeling diffusion on
social networks. This
example will also show why and when ABM
is needed and will highlight the relationship between ABM and a more
traditional
aggregate system dynamics model (10). Let us assume a new product's value V depends on the number of its users, N, in a total population of N
T potential adopters, according to the following function
where ρ is the fraction of the population that has adopted the product, θ is a characteristic value (here θ = 0.4), and
d is an exponent that determines the steepness of the function (here d = 4). V(N)
equals 0 when there is no user and is maximum (= 1) when the entire
population has adopted the product. Finally, θ acts
as a threshold: when the user base
approaches 40% of the population, the value curve takes off. Let us
assume for simplicity
that the value function is the same for
all users. Let us further assume that the adoption rate is given by an
estimate
of V by potential customers.
Indeed, customers may not know the exact number of people who have
adopted the technology in the
population, but they can estimate the
fraction of users in their social neighborhood. If we assume that each
person is connected
to n other people in the population, we can define person k's estimate of the fraction of users in the entire population as ρ̂k = nk
/n, where nk
is the number of k's neighbors who have adopted the product. The value V̂k
of the product, as estimated by person k, is then given by
If person k is connected to everyone else, V̂k
is identical to V. However, that is unlikely. A system dynamics approach to the problem would model the flow of people from nonusers to users,
with every person in the population perceiving the same average fraction of adopters ρ = N/N
T and therefore the same perceived value:
The resulting differential equation is
which is equivalent to
We assume here that the time unit is 10 days. Fig. 3
a shows how ρ and V vary in time, when the initial number of users is equal to 5% of the population.
where ρ is the fraction of the population that has adopted the product, θ is a characteristic value (here θ = 0.4), and
d is an exponent that determines the steepness of the function (here d = 4). V(N)
equals 0 when there is no user and is maximum (= 1) when the entire
population has adopted the product. Finally, θ acts
as a threshold: when the user base
approaches 40% of the population, the value curve takes off. Let us
assume for simplicity
that the value function is the same for
all users. Let us further assume that the adoption rate is given by an
estimate
of V by potential customers.
Indeed, customers may not know the exact number of people who have
adopted the technology in the
population, but they can estimate the
fraction of users in their social neighborhood. If we assume that each
person is connected
to n other people in the population, we can define person k's estimate of the fraction of users in the entire population as ρ̂k = nk
/n, where nk
is the number of k's neighbors who have adopted the product. The value V̂k
of the product, as estimated by person k, is then given by
If person k is connected to everyone else, V̂k
is identical to V. However, that is unlikely. A system dynamics approach to the problem would model the flow of people from nonusers to users,
with every person in the population perceiving the same average fraction of adopters ρ = N/N
T and therefore the same perceived value:
The resulting differential equation is
which is equivalent to
We assume here that the time unit is 10 days. Fig. 3
a shows how ρ and V vary in time, when the initial number of users is equal to 5% of the population.
Fig. 3.
(a) Differential equation results. (b) Mean-field agent-based model.
-
Those 30 neighbors are selected randomly in the population.
-
There is clustering in the topology of social interactions in that a neighbor of a neighbor is likely to be a neighbor. For definiteness, I will assume that the population is divided into two subpopulations of equal size. The probability that two individuals from the same subpopulation are neighbors is equal to P = 0.5, and the probability that two individuals from different subpopulations are neighbors is equal to 0.1. In a population of 100 agents, the average total number of neighbors of any given node is 0.5⋅50 + 0.1⋅50 = 30. We assume that the initial 5% of users is within one of the subpopulations.
The second case introduces
localization in the dynamics: a person interacts only with her
neighbors and there are few long-range
interactions and little global mixing. In
the first case, one might expect to observe a dynamics similar to the
system dynamics
model, whereas the dynamics in the second
case could be quite different. It appears that even in the first case
the resulting
dynamics is different from the mean-field
dynamics (Fig. 4
a), but the second case leads to potentially dramatically different results, as can be seen in Fig. 4
b. Product adoption is a lot faster with clustering, even when the initial user population is located entirely within one
cluster.
Fig. 4.
(a) One hundred agents, 30 random neighbors. (b) One hundred agents, clustered neighbors (two clusters, spread starting in one cluster).
This simple example shows not
only how useful ABM is when dealing with inhomogeneous populations and
interaction networks
but also how to go from a differential
equation model to an agent-based model—usually it is the opposite
transformation
that is used, where the differential
equation model is the analytically tractable (but deceivingly so)
mean-field version
of the agent-based model. What is useful
about this “reverse” transformation is that it clearly shows that an
agent-based
model is increasingly necessary as the
degree of inhomogeneity increases in the modeled system.
Discussion
When Is ABM Useful?
It should be clear from the examples presented in this article that ABM can bring significant benefits when applied to human
systems. It is useful at this point to summarize when it is best to use ABM:
-
When the interactions between the agents are complex, nonlinear, discontinuous, or discrete (for example, when the behavior of an agent can be altered dramatically, even discontinuously, by other agents). Example: all examples described in this article.
-
When space is crucial and the agents' positions are not fixed. Example: fire escape, theme park, supermarket, traffic.
-
When the population is heterogeneous, when each individual is (potentially) different. Example: virtually every example in this article.
-
When the topology of the interactions is heterogeneous and complex. Example: when interactions are homogeneous and globally mixing, there is no need for agent-based simulation, but social networks are rarely homogeneous, they are characterized by clusters, leading to deviations from the average behavior.
-
When the agents exhibit complex behavior, including learning and adaptation. Example: NASDAQ, ISPs.
Issues with ABM.
There
are some issues related to the application of ABM to the social,
political, and economic sciences. One issue is common
to all modeling techniques: a model has
to serve a purpose; a general-purpose model cannot work. The model has
to be built
at the right level of description, with
just the right amount of detail to serve its purpose; this remains an
art more than
a science.
Another issue has to do with the
very nature of the systems one is modeling with ABM in the social
sciences: they most often
involve human agents, with potentially
irrational behavior, subjective choices, and complex psychology—in
other words, soft
factors, difficult to quantify,
calibrate, and sometimes justify. Although this may constitute a major
source of problems
in interpreting the outcomes of
simulations, it is fair to say that in most cases ABM is simply the
only game in town to
deal with such situations. Having said
that, one must be careful, then, in how one uses ABM: for example, one
must not make
decisions on the basis of the quantitative
outcome of a simulation that should be interpreted purely at the
qualitative level.
Because of the varying degree of accuracy
and completeness in the input to the model (data, expertise, etc.),
the nature
of the output is similarly varied,
ranging from purely qualitative insights all the way to quantitative
results usable for
decision-making and implementation.
The last major issue in ABM is a
practical issue that must not be overlooked. By definition, ABM looks
at a system not at
the aggregate level but at the level of
its constituent units. Although the aggregate level could perhaps be
described with
just a few equations of motion, the
lower-level description involves describing the individual behavior of
potentially many
constituent units. Simulating the behavior
of all of the units can be extremely computation intensive and
therefore time
consuming. Although computing power is
still increasing at an impressive pace, the high computational
requirements of ABM
remain a problem when it comes to modeling
large systems.
Footnotes
-
* E-mail: eric@icosystem.com.
-
This paper results from the Arthur M. Sackler Colloquium of the National Academy of Sciences, “Adaptive Agents, Intelligence, and Emergent Human Organization: Capturing Complexity through Agent-Based Modeling,” held October 4–6, 2001, at the Arnold and Mabel Beckman Center of the National Academies of Science and Engineering in Irvine, CA.
- Abbreviations:
-
ABM, agent-based modeling
-
NASDAQ, National Association of Security Dealers Automated Quotation
-
ISP, Internet service provider
-
- Copyright © 2002, The National Academy of Sciences
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