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5
Micro-Level Formal Models
I
n this chapter we discuss several micro-level formal models of human
behavior, models that most often are concerned with the behavior
of individuals. We begin with cognitive architectures, followed by
cognitive-affective models that consider the effect of human emotions
on cognition and behavior, as well as of behavior on emotions. We then
discuss expert systems, a legacy modeling approach that provides a frame-
work for representing human expertise, and that now is often used as a
programming paradigm in decision aiding systems. Finally we discuss
decision theory and game theory and their limited applicability to indi-
vidual, organizational, and societal modeling in general.
For each model or approach, we follow the same discussion framework
as in Chapters 3 and 4: we present the current state of the art, the most
common applications of the approach, its strengths and limitations for the
problems described in Chapter 2, and suggestions for further research and
development.
COgNITIvE ARCHITECTuRES
Cognitive architectures are simulation-based models of human cog-
nition. Their distinguishing feature is the broad focus on modeling the
full sequence of information processing (stimulus-to-behavior) mediating
adaptive, intelligent behavior. Cognitive architectures are built both for
basic research and for applied purposes. Different architectures typically
emphasize distinct aspects of human cognition (e.g., memory, multitasking,
4
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50 BEHAVIORAL MODELING AND SIMULATION
attention, learning, etc.), depending on their research objectives or applica-
tion goals.1
Typically, cognitive architectures are used to model individual cogni-
tion. Less often, the applicability of this approach for modeling collective
behavior has also been explored, that is, using a cognitive architecture
to model the behavior of a group, team, or organization. The utility and
appropriateness of this approach to modeling group cognition has yet to
be demonstrated, however,2 and so we have restricted our discussion here
to covering the use of individual cognitive architectures to the modeling of
individual behavior.
Cognitive architectures have their roots in the early artificial intelligence
(AI) models of human problem solving developed in the 1950s. These mod-
els combined a number of key ideas emerging from observations of human
problem solving and behavior, including symbolic processing, hierarchical
organization of goals, problem spaces, rule- and heuristic-based behavior,
and parallel and distributed representation and computation.
A number of cognitive models were developed in the 1970s and
1980s, such as the Model Human Processor (MHP) and Goals, Operators,
Methods, and Selection rules (GOMS) (Card, Moran, and Newell, 1986),
focusing on modeling a single function in the context of a single task and
most often applied to models of human-computer interaction and, in par-
ticular, to the design and evaluation of user interfaces. Although limited in
scope, these models provided the necessary methodological foundations for
the more broadly scoped cognitive architectures of today, by demonstrating
the feasibility and benefits of computational cognitive models, primarily in
the context of human-computer interface design.
What Are Cognitive Architectures?
Cognitive architectures are computational, simulation models of
human information processing and behavior. Cognitive architectures are
also referred to as agent architectures, computational cognitive models, and
human behavior models.3 These simulation-based models aim to implement
1 Indeed, this report’s focus on models and simulations that can contribute to some element
of improving forecasting or explanation in a Department of Defense context may limit the
ultimate utility of applying some of the models described herein (and elsewhere in the report)
in a broader nonmilitary context. Some researchers may argue that this is not the case because
of inherent model generality, but this general issue goes beyond the original scope of the study
and clearly deserves further study.
2 Researchers are beginning to suggest future work in this area; see, for example, MacMillan
(2007).
3 Specific connotations may exist with each of these terms regarding the motivation and use
of the cognitive architecture.
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5
MICRO-LEVEL FORMAL MODELS
some version of a unified theory of cognition (Newell, 1990) by modeling
the entire end-to-end human information-processing sequence, beginning
with the current set of stimuli and ending with a specific behavior.
Cognitive architectures are typically classified into three broad cat-
egories, depending on their approach to knowledge representation and
inferencing: symbolic, subsymbolic (also referred to as parallel-distributed),
or hybrid (combining elements of the former two). Symbolic architectures
use one or more propositional knowledge representation formalisms, such
as rules, belief nets, or semantic nets. Subsymbolic, parallel-distributed
architectures typically use some type of a connectionist representation and
inferencing (e.g., recurrent neural networks), in which the mapping between
conceptual entities and the representation is not one-to-one, because the
knowledge is distributed over multiple representational elements (e.g.,
nodes within the network). Hybrid architectures use elements of both rep-
resentational formalisms and are becoming increasingly common, as the
benefits of the combined symbolic-subsymbolic knowledge representation
and inferencing are recognized.
The specific functions represented in a particular architecture depend on
its objective, level of resolution, and theoretical underpinnings. These also
determine the specific modules that make up a given architecture. In most
symbolic architectures, the modules and process structure correspond to (a
subset of) the functions comprising human information processing. Most
architectures thus contain some subset of the following broad cognitive and
perceptual processes: attention, situation assessment, goal management,
planning, metacognition, learning, action selection, and necessarily some
form of memory (or memories), such as sensory, working, and long-term.
Thus, for example, an architecture attempting to model recognition-
primed decision making (RPD) would have a module dedicated to situation
assessment, since that is a core component of the RPD theory (Klein, 1997);
an architecture focusing on models of learning would have corresponding
modules responsible for such functions as credit assignment and creation of
new schemas in memory. It should be noted here that most existing cogni-
tive architectures are not capable of learning (Morrison, 2003). While some
architectures, such as Soar, do contain elements of learning (e.g., creation
of new operators by combining existing operators), typically, there is no
direct learning resulting from the agent’s interactions with the environment.
However, the cognitive modeling community is beginning to recognize the
limitations of human-constructed long-term memories in these models, and
researchers are beginning to address the problem of automatic knowledge
acquisition and learning in cognitive architectures (e.g., Anderson et al.,
2003; Langley and Choi, 2006).
Depending on the architecture’s control structure, the modules may
execute in a fixed sequence, or in parallel, or anywhere between these two
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5 BEHAVIORAL MODELING AND SIMULATION
extremes. Figure 5-1 illustrates the module structure of a notional sequen-
tial cognitive architecture, frequently referred to as a “see-think-do” control
structure. An alternative to this sequential approach is a parallel-distributed
control structure, in which a number of parallel processes access a com-
mon memory structure (frequently referred to as a blackboard and hence
the term “blackboard architectures,” Corkill, 1991). As with the sequential
architectures, the specific processes represented, as well as the structure of
the memory blackboard, depend on the architecture objectives, the level
of resolution, and theoretical foundations. Figure 5-2 shows an example
of a blackboard architecture, illustrating examples of possible associated
processes. Historically, cognitive architectures have focused on the middle
stage of the see-think-do metaphor, frequently simplifying the perceptual
input and motor output components. However, as cognitive architectures
expand in model complexity and desired functionality (e.g., operating in a
real-world environment), they increasingly incorporate sensory and motor
models to become full-fledged agent architectures, capable of autonomous,
intelligent, and adaptive behavior in a real or a simulated world.
Cognitive architectures thus contrast with the more narrowly scoped
cognitive models (also referred to as micro models of cognition), which
Sensing and Cognition
Perception • Multitasking
• Memory and Learning
• Attention
Working Motor
• Situation Awareness
• Vision Memory Behavior
• Decision Making
• Hearing
• Planning
• Perception
• Behavior Moderators
Long-Term Memory
Stimuli Responses
Goals / Tasks
World
Maintain situation awareness
Model
Other Report important events
declarative
Assess threat to goals
knowledge
Assess alternatives
Manage goals / tasks
Procedural
knowledge
External world events
5-1.eps
FIguRE 5-1 Example of a notional sequential cognitive architecture.
The word “Cognition” in the 3rd box from left,
at top, was set in 1-pt text--too small to see.
Word doc would not open.
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5
MICRO-LEVEL FORMAL MODELS
Situation Goal Action
Planning
Assessment Selection Selection
Visual
Sensor
Right hand
Auditory
Blackboard
Blackboard
Sensor
Left hand
Gaze
FIguRE 5-2 A blackboard architecture.
5-2.eps
focus on a single function, such as attention, visual search, visual percep-
tion, language acquisition, or memory recall and retrieval, and implement
micro theories of cognition, rather than unified theories of cognition.
This figure shows a high-level view of a parallel-distributed cognitive
architecture, which represents an alternative to the sequential see-think-
do model. In parallel-distributed models, processing occurs in multiple,
concurrent processes, and coordination among these processes is achieved
through the intermediate results posted on the blackboard, which represents
the architecture memory. The structure of the blackboard varies, depend-
ing on a particular architecture, to represent the desired types of distinct
memories.
State of the Art
A large number of cognitive architectures have been developed in both
academic and industrial settings, and new architectures are rapidly emerg-
ing due to increasing demand, particularly in human-computer interaction
(HCI) and decision support contexts, with emphasis on training, decision
aiding, interactive gaming, and virtual environments. Three recent reviews
provide a comprehensive catalogue of a number of established or commer-
cially available cognitive architectures: a report focusing on U.S.-developed
systems (Andre, Klesen, Gebhard, Allen, and Rist, 2000, pp. 51–111), a
supplementary report focusing on systems developed in Europe, primarily
in the United Kingdom (Ritter et al., 2003), and a review by Morrison that
covers architectures in both the United States and Europe and includes some
of the lesser known systems (Morrison, 2003). All three reviews provide
detailed descriptions of the architectures in terms of the cognitive processes
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54 BEHAVIORAL MODELING AND SIMULATION
modeled, their historical context, applications, and implementation lan-
guages and any validation studies. A large number of research-oriented
architectures also exist in laboratories around the world. The best sources
for information regarding these architectures are conferences and work-
shops, such as the International Conference on Cognitive Modeling, the
annual meeting of the Cognitive Science Society, symposia and conferences
of the American Association for Artificial Intelligence, Autonomous Agents
and Multi-Agent Systems, Human Factors, and BRIMS. See Table 2-1 for
an overview of cognitive architectures used in military contexts.
Existing cognitive architectures are being used to support research on
both human cognition and, more recently, emotion (see the next section
on cognitive-affective models). They are also used in applied settings to
control the behavior of synthetic agents and robots in a variety of contexts,
including gaming and virtual reality environments, to enable user modeling
in adaptive systems, and as replacements for human users and subjects for
training, assessment, and system design purposes.
It is beyond the scope of this chapter to describe in detail the large
number of architectures that have been developed over the past 25 years.
The three reviews mentioned above are excellent sources of in-depth infor-
mation regarding a number of architectures that are sufficiently estab-
lished to be included in comprehensive reviews. Below we briefly discuss
a subset of these, to provide a sense of the breadth of theoretical ori-
entations, representational formalisms and modeling methodologies, and
applications.
It should be noted that each architecture elaborates a particular sub-
set of cognitive processing and that the architectures vary in their ease of
transition to other domains and ease of use. These factors must be taken
into consideration when a particular architecture is being considered as a
modeling tool for a specific problem in a particular domain. For example,
ACT-R’s focus is on relatively low-level processing, and is particularly con-
cerned with memory modeling. EPIC emphasizes models of multitasking.
Soar emphasizes a particular model of learning, cast in relatively high-level
symbolic terms. Thus, before a particular architecture is adopted for a spe-
cific modeling effort, it is necessary to carefully assess its ability to model
the processes of interest at the desired level of resolution.
The most established architectures in the United States are ACT-R and
Soar, each having a large and active academic research community, with
annual workshops and tutorials, and each having an increasing presence
in industry, primarily the defense industry. These are described below,
followed by several other prominent architectures.
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MICRO-LEVEL FORMAL MODELS
ACT-R
The historical focus of ACT-R (Atomic Components of Thought or
Adaptive Character of Thought) has been on basic research in cognition
and modeling of a variety of fundamental psychological processes, such as
learning and memory (e.g., priming) (Anderson, 1983, 1990, 1993). ACT-R
combines a semantic net representation with rule-based representation to
support declarative and procedural memory representation and associated
inferencing. ACT-R is probably the cognitive architecture that is “best
grounded in the experimental research literature” (Morrison, 2003, p. 24).
Primary early applications were tutoring in mathematics and computer pro-
gramming (see www.carnegielearning.com). Gradually, ACT-R evolved into
a full-fledged cognitive architecture, with increasing emphasis on sensory
and motor components and applications in military settings (e.g., modeling
adversary behavior in military operations on urban terrain, MOUT, tactical
action officers in submarines, radar operators on ships; Andre et al., 2000;
Anderson et al., 2004).
Soar
Soar (State, Operator, and Results) development was initially motivated
by the desire to demonstrate the ability of generalized problem spaces, rules,
and heuristic search capabilities to solve a wide range of problems and by
the desire to develop an implementation of the unified theory of cognition
of Newell (1990). Soar uses production rules to implement this problem-
solving paradigm, via application of “operators” to states within a problem
space. Soar represents all three types of long-term memory (declarative,
procedural, and episodic) in terms of rules. A distinguishing feature of Soar
is its ability to form new operators (rules) from existing operators (rules),
when it reaches an impasse in its problem solving (impasse being defined
as either no applicable operators selected or conflict among operators). It
is thus one of the few architectures that explicitly addresses learning, albeit
in the limited context of combining existing elements within its own knowl-
edge base, rather than the bona fide acquisition of new knowledge from its
interaction with the environment. Soar models both reactive and delibera-
tive reasoning and is capable of planning (Hill, Chen, Gratch, Rosenbloom,
and Tambe, 1998).
While Soar was in part motivated by theoretical considerations, par-
ticularly Newell’s unified theory of cognition, the architecture has become
a more traditional AI system, in its increasing emphasis on performance,
rather than accurate emulation of human information processing. A fre-
quent criticism of Soar is its large number of free variables, which enables
a large number of specific models to match empirical data, thereby making
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5 BEHAVIORAL MODELING AND SIMULATION
it difficult to unequivocally establish the validity of a given model. This is
the case with most computational cognitive architectures.
Soar’s capabilities progressed from simple toy tasks (puzzles), through
expert systems applications (medical diagnosis, software design), to archi-
tectures capable of controlling autonomous agents. Soar represents the more
extensively applied cognitive architecture and includes a number of training
installations or exercises in which it has replaced human role players or
autonomous air entities: TacAir-Soar at the Air Force Research Laboratory
(AFRL) training laboratory and at Williams Air Force Base (fixed-wing
missions), Joint Forces Command (JFCOM) J9 exercises, MOUTBot (sol-
dier models) VIRTE MOUT at the Office for Naval Research, JCATS at the
Defense Modeling and Simulation Office; SOFSoar at JFCOM, RWA-Soar
(rotary wing missions), STEVE for training simulations, and Quakebot for
interactive computer games (Jones et al., 1999; Laird, 2000). The applica-
tions in the military are being developed by Soar Technology, Inc. (http://
www.soartech.com). Soar also serves as the core technology at the Institute
for Creative Technologies at the University of Southern California, where
it acts as an agent architecture, controlling synthetic characters in virtual
environments, primarily applied to training and game-based training envi-
ronments. Soar has also been applied in a nondefense context, to develop
a decision support system for businesses (KB Agent, developed by ExpLore
Reasoning Systems, Inc.).
While the emphasis in Soar applications has been on individual models,
it has also been applied in modeling multiagent environments, in which
explicit representations exist of shared structures among team members
(e.g., goals, plans). The STEAM model (Shell for TEAMwork) (1996)
implements these enhancements and has been applied to military simula-
tions (models of helicopter pilots) and to modeling soccer players in the
RoboCup competition (Tambe et al., 1999).
EPIC
EPIC (Executive-Process/Interactive Control), developed from the MHP
(Card et al., 1986), focuses on models of human behavior in multitasking
contexts, in human-computer interaction. A distinguishing feature is its
emphasis on integrating cognition with perceptual and motor processes.
EPIC’s sensorimotor capabilities have motivated its inclusion in some Soar
models, to provide an interface with the real world. EPIC uses production
rules to represent both its long-term memory and the control of processing
within the architecture. It is primarily focused on research and is a good
example of a more constrained architecture with a strong focus on valida-
tion against human performance data. Recently EPIC has also been used in
more applied settings, for the design of undersea ship systems.
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MICRO-LEVEL FORMAL MODELS
COgNET
COGNET (COGnition as a Network of Tasks) architecture was devel-
oped by CHI Systems and combines several knowledge representation
formalisms in a blackboard-oriented framework. It was initially applied
in user interface design (Zachary, Jones, and Taylor, 2002) but has been
expanded to include models of multitasking in the context of air traffic con-
trol (Zachary, Santarelli, Ryder, Stokes, and Scolaro, 2001) and intelligent
tutoring (Zachary et al., 1999). COGNET has an associated development
environment iGEN, which is commercially available from CHI Systems.
OMAR
OMAR (Operator Model Architecture) is a task-goal network model
with a focus on multitasking developed by BBN, Inc. (Deutsch, Cramer,
Keith, and Freeman, 1999), from an earlier conceptual prototype, the
CHAOS model (Hudlicka, Adams, and Feehrer, 1992). OMAR and its
later distributed version, D-OMAR, have been used to model air traffic
control and pilot error (Deutsch et al., 1999; Deutsch and Pew, 2001). It
was one of the systems participating in the AMBR (Agent-based Modeling
and Behavior Representation) validation project, in which its performance
was compared with other cognitive architectures and with human subjects
in the context of air traffic control (Gluck and Pew, 2005). Recent versions
of OMAR were expanded with models of auditory and visual inputs, and
the system was reimplemented in Java (from the original LISP version), to
improve performance.
MIDAS
MIDAS (Man-machine Integrated Design and Analysis System) uses
a goal-task network model to model simple, reactive decision making. It
includes sensory inputs (visual and auditory) and simple motor outputs and
has been applied in human-computer interaction to model pilot behavior in
support of cockpit design (Corker and Smith, 1992; Corker, Gore, Fleming,
and Lane, 2000; Laughery and Corker, 1997), air traffic control, the design
of emergency communication systems, and the design of automation sys-
tems for nuclear power plants. MIDAS is also capable of modeling multiple,
interacting agents.
SAMPLE
SAMPLE (Situation Awareness Model for Pilot-in-the-Loop Evalua-
tion) is a sequential hybrid model developed by Charles River Analytics,
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5 BEHAVIORAL MODELING AND SIMULATION
using several knowledge representational mechanisms, including fuzzy logic
and belief nets and rules. It has been applied to model air traffic control,
pilot behavior, unmanned aerial vehicles, and soldier behavior in MOUT
operations (Zacharias, Miao, Illgen, and Yara, 1995; Harper, Ton, Jacobs,
Hess, and Zacharias, 2001). SAMPLE implements the recognition-primed
decision-making model (Klein, 1997) and does not include complex plan-
ning. Sensorimotor components are represented at highly abstracted levels.
SAMPLE has a drag-and-drop development environment GRADE, for rapid
application prototyping, and is available commercially.
APEX
APEX is an architecture supporting the creation of intelligent, autono-
mous systems and serves also as a development environment. One of its
goals is to reduce the effort required to develop agent architectures. Its
primary applications are in human-computer interaction, to help design
user interfaces and human-machine systems (Freed, Dahlman, Dalal, and
Harris, 2002), and it has been applied in air traffic control.
Other Architectures
Several other architectures should be mentioned briefly. D-COG
(Distributed Cognition) was developed at AFRL (Eggleston, Young, and
McCreight, 2000) to model complex adaptive behavior. It was one of the
architectures evaluated in the AMBR experiment (see Validation below).
BRAHMS (Business Redesign Agent-Based Holistic Modeling System) is
an environment developed by the National Aeronautics and Space Admin-
istration (NASA) for modeling multiple, interacting entities (Sierhuis and
Clancey, 1997; Sierhuis, 2001) and emphasizes the interaction among
entities rather than individual cognition.
Several well-established cognitive architectures have been developed in
Europe. COGENT (Cognitive Objects within a Graphical EnviroNmentT)
is a development environment for construction cognitive models developed
by Cooper and colleagues (Cooper, Yule, and Sutton, 1998; Cooper, 2002).
It supports the construction of cognitive architecture from individual, inde-
pendent “modules,” each responsible for a particular cognitive (or percep-
tual) function, and includes explicit support for systematic evaluation of
the resulting models. COGENT offers a number of representational formal-
isms, including connectionist formalisms supporting the representation of
distributed, subsymbolic knowledge. It has been applied to model medical
diagnosis, models of memory, and models of concept learning.
The architectures outlined above are primarily symbolic and represent
the most common approach to the development of integrated cognitive
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MICRO-LEVEL FORMAL MODELS
architectures. There are also examples of architectures that use connec-
tionist formalisms, either exclusively or in combination with symbolic
representations. We briefly mention two of these below. An example of the
former is the ART (Adaptive Resonance Theory) architecture, developed
by Grossberg (1999, 2000). ART emphasizes learning and parallel process-
ing, both being key benefits of connectionist formalisms. An example of a
hybrid connectionist-symbolic architecture is CLARION (Connectionist
Learning with Adaptive Rule Indication On-Line), developed to support
research in combined representations of symbolic knowledge (via rules) and
subsymbolic knowledge (via connectionist networks) and inductive learning
(Sun, 2003, 2005).
Current Trends
Several current trends in cognitive architecture development promise
to contribute to more efficient development of these complex simulation
systems, as well as more effective applications:
• Efforts to incorporate individual differences and behavior mod-
erators, such as personalities and emotions, both to support basic
research and to produce more realistic and robust agents (see next
section).
• Efforts to provide broadly scoped end-to-end architectures, with
increasing emphasis on sensory and motor processes, to enable the
associated synthetic agent or robot to function in a virtual or actual
environment (e.g., variety of Soar-based agents being developed at
the Institute for Creative Technologies).
• Use of shared ontologies to facilitate the labor-intensive effort of
cognitive task analysis and domain-specific model construction.
• Use of development environments to facilitate cognitive architec-
ture construction, which may include automatic KA/KE facilities,
visualizations, and model performance assessment and analysis
tools.
• Increasing emphasis on empirical validation, frequently with respect
to human performance data, and the development of validation
methodologies and metrics (e.g., Gluck and Pew, 2005).
verification and validation Issues
As stated above, verification refers to ensuring that the architecture
functions as intended, that is, that the model has been implemented accord-
ing to the specifications. Validation refers to the degree to which the model
specifications reflect the reality, at the desired level of resolution. We focus
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04 BEHAVIORAL MODELING AND SIMULATION
described by Colonel Blotto but nevertheless informed by Colonel Blotto.
However, as we have noted, the severe limitations of decision theory and
game theory make this move to a more elaborate and realistic model
impractical and not as trivial a step as the formal theorists might wish.
Game theory has been of moderate use in analyzing institutions. The
game theoretic approach consists of four steps (Diermeier and Krehbiel,
2003):
1. Assume behavior.
2. Define the game generated by the institution.
3. Deduce the equilibria.
4. Compare the regularities to data.
If behavior is assumed to be optimizing, then equilibrium is achieved
and institutions can be thought of as equivalent to equilibria. To compare
two institutions, we need only compare their equilibria: the better the equi-
librium (e.g., the greater utility to the relevant actors), the better the institu-
tion, and the more the actors will prefer it. The institutions as equilibrium
approach proves powerful. If we want to compare a parliament with an
open rule system, in which anyone can make a proposal, with a closed rule
system, in which amendments are not allowed, or to compare a parliamen-
tary system with a presidential system, we construct models of the two
types of institution and compare their equilibria using game theory (Baron
and Ferejohn, 1989). The institutions as equilibrium approach of game
theory can be extended to include the game over institutions. In this game,
the players first decide which institution to use. This meta-institutional
game can explain not only how institutions perform but also why they may
have been chosen in the first place. For example, we might use such a model
to explain why a military leader chooses an open rule system even though
that system allows greater voice to members of his cabinet. However, as
noted, the assumptions that need to be made here are highly unrealistic,
hence calling the entire approach into question.
When we expand game theory to include learning models, then we can
capture some forms of cultural transference. Many game theorists think of
culture as beliefs. That characterization provides some leverage, but it is
far from adequate. More recent work considers cultural learning in which
players learn from one another (Gintis, 2000). They can even learn from
the other games that they play (Bednar and Page, 2007). Game theoretic
models can also be expanded to include networks that can evolve over time.
In sum, game theoretic models can include cultural forces, but those forces
must be well defined and analytically tractable. The movement to expand
game theory by taking networks and culture into account is promising.
However, the research here is in its infancy.
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MICRO-LEVEL FORMAL MODELS
Major Limitations
Decision theory models and game theory models tend to be overly sim-
plistic, with few “moving parts” and with assumptions made with regard
to the player behavioral characteristics that can be driven more by ease of
solution criteria rather than fidelity of representation. Otherwise, the models
become difficult or impossible to solve. For example, most game theory
models assume either two players or an infinite number of players. The
real world often takes place in the space in between, except for extremely
artificial situations (e.g., chess games, two-candidate political races, etc.).
Decision theory and game theory models require data about actors that
often cannot be gathered with any reliability or within a reasonable amount
of time determined by the decision window of the commander.
A further problem with game theory models is that they produce mul-
tiple equilibria. The Folk Theorem result states that, for repeated games,
almost any outcome can be supported as an equilibrium. To overcome this
problem of multiple equilibria, game theorists rely on refinements, such as
symmetry. An equilibrium is symmetric if both players get the same payoff.
Or they invoke Pareto efficiency: an equilibrium is Pareto efficient if no
other equilibrium makes every player better off. Game theoretic models
also often ignore the stability and attainability of the equilibria that they
predict. Although recently game theorists have begun to study learning
models, they tend to consider simple two-person games and not the more
complex, multiplayer situations characteristic of the real world.
Future Research and Development Requirements
The potential for decision theory and game theory hinges on their
ability to capture the complexities of real people and the real world. A
concern with realism would seem to undercut the mathematical strength
of these two approaches: their ability to cut to the heart of a situation.
Nevertheless, the few degrees of freedom that these models allow can be
tugged in the direction of greater realism with potentially large benefits.
In decision theory, we can look to cultural and cognitive explanations to
explain beliefs. We can also look to culture as a determinant of what is pos-
sible: some actions may be unlikely to occur in some cultures. Therefore, we
can rule those actions out. However, as decision theory and game theoretic
models become more nuanced to include cultural factors, they become
less mathematically tractable, require increased data or more unrealistic
assumptions, and require more effort for validation.
As already mentioned, game theorists have begun including culture in
the form of beliefs, networks, and behaviors. This can also be accomplished
less formally. For example, Calvert and Johnson (1999) argue for culture
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0 BEHAVIORAL MODELING AND SIMULATION
as a means of coordinating on an equilibrium. By coordination, they mean
selection of one equilibrium from among many. In their approach, game
theory becomes a preliminary tool: it defines the set of possible outcomes.
Detailed historical and cultural knowledge from subject matter experts then
selects from among those equilibria.
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