Comput Math Organ Theory (2015) 21:115–149
DOI 10.1007/s10588-014-9179-0
Building social networks out of cognitive blocks: factors
of interest in agent-based socio-cognitive simulations
Changkun Zhao • Ryan Kaulakis •
Jonathan H. Morgan • Jeremiah W. Hiam
Frank E. Ritter • Joesph Sanford •
Geoffrey P. Morgan
•
Published online: 27 December 2014
! Springer Science+Business Media New York 2014
Abstract This paper examines how cognitive and environmental factors influence
the formation of dyadic ties. We use agent models instantiated in ACT-R that
interact in a social simulation, to illustrate the effect of memory constraints on
networks. We also show that environmental factors are important including population size, running time, and map configuration. To examine these relationships, we
ran simulations of networks using a factorial design. Our analyses suggest three
interesting conclusions: first, the tie formation of these networks approximates a
logistic growth model; second, that agent memory quality (i.e., perfect or humanlike) strongly alters the network’s density and structure; third, that the three
C. Zhao (&) ! R. Kaulakis ! J. W. Hiam ! F. E. Ritter
The College of Information Sciences and Technology, The Pennsylvania State University,
State College, USA
e-mail: [email protected]
R. Kaulakis
e-mail: [email protected]
J. W. Hiam
e-mail: [email protected]
F. E. Ritter
e-mail: [email protected]
J. H. Morgan
Department of Sociology, Duke University, Durham, USA
e-mail: [email protected]
J. Sanford
Department of Computer Science, Tufts University, Medford, USA
e-mail: [email protected]
G. P. Morgan
School of Computer Science, Carnegie Mellon University, Pittsburgh, USA
e-mail: [email protected]
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environmental factors all influence both network density and some aspects of network structure. These findings suggest that meaningful variance of social network
analysis measures occur in a narrow band of memory strength (the cognitive band);
the threshold for defining tie criteria is important; and future simulations examining
generative social networks should control and carefully report these environmental
and cognitive factors.
Keywords
Cognitive simulation ! ACT-R ! Dunbar’s number ! Social cognition
1 Introduction
Anderson argues that ‘large-scale learning in groups arises from of small-scale
learning’ (2002, p. 87). This paper explores that thesis by examining how cognitive
and environmental factors influence the formation and resulting structure of social
networks. We do this by varying these factors and seeing how they affect the
formation of dyads in networks. This work is motivated by a desire to better
understand how socio-cognitive processes influence the development of persistent
patterns of relations. By socio-cognitive processes, we refer to both those cognitive
resources and mechanisms necessary to create and sustain social ties, as well as
those group-level factors known to moderate human decision-making (Morgan and
Carley 2011; Morgan et al. 2010; Silverman 2004; Yen et al. 2001). We focus on
memory retention and navigation patterns in this paper because these two processes
seem foundational to understanding the emergence of social networks in a variety of
contexts.
To explore these relationships, we introduce one simulation environment, two
agent-based models, two experiments, and three analyses that examine the influence
of memory, population size, run time, map configuration, and agent navigation. The
simulation environment outputs both interaction networks, a matrix showing the
total number of agent co-occurrences in the simulation, and ego-nets, weighted
declarative representations of each agents’ friends network. For any one run, there is
one interaction network and as many ego-nets as there are agents in the experiment.
We merge the individual ego-nets to examine how each factor influences the
generation process and structure of the resulting network.
We start by reviewing previous work in social and cognitive modeling related to
social network growth and structure.
1.1 Related previous work using simulations
Researchers have developed agent-based models to explore a variety of questions.
We briefly examine two major, related, agent-based, modeling approaches:
cognitive modeling and social modeling. These approaches are not necessarily
mutually exclusive. However, combined socio-cognitive models are relatively rare
because they are generally expensive to create and run.
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Factors of interest in agent-based socio-cognitive simulations
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Social simulation is a large category that includes both computational and
graphical models. Computational social simulation models such as those in the
Complex Systems literature frequently, but not always, use boundedly rational
agents (Conte et al. 2014; Holland 1992; Miller and Page 2007). Boundedly rational
agents are limited both cognitively and socially (Simon 1991). These models can
feature entities that range from simple rule-defined automata to goal-driven agents.
What unifies these approaches is the use of agents to understand the emergence of
system-level properties, generally by showing how past states condition future
states. In these models, system-level behaviors arise out of the agents’ discrete
interactions, but cannot be explained entirely with reference to them. Further, at
different levels of observation, different kinds of emergent behavior can be seen. It
is often these kinds of traits that simulations are uniquely able to capture.
Early work in social simulation includes Schelling’s (1971) segregation model,
Axelrod and Hamilton’s (1981) work on cooperation, and Epstein and Axtell’s
(1996) Sugarscape simulations. More recently, increases in computational power
have led to a renewed interest in multi-level modeling (Epstein 2006) specifically
simulating the influence of dynamics occurring at one level of analysis (e.g., the
small group level) on others (e.g., individuals or organizations). For instance,
Barrett et al. (2006) model the influence of paths in crisis situations using large
simulations featuring millions of agents, allowing them to identify emergent effects
at the community level.
Cognitive modeling, emerging at roughly the same time as work in social
simulation, has attempted to model computationally the effects of perception and
memory by simulating cognitive functions. To our knowledge, Carley and Newell
(Carley 1991, 1992; Newell 1990; Newell et al. 1989; Carley et al. 1990) were the
first to study organizations using models based on a cognitive architecture. For
example, they created a warehouse simulation (Carley et al. 1990) with multiple
(n = 1–5) boundedly rational agents to examine the influences of group size on
joint task performance. More recently, Reitter and Lebiere (2010, 2011) created an
agent-based simulation (ACT-UP) that includes the basic mechanisms of ACT-R
theory. ACT-UP focuses on examining the cognitive factors in real-world scenarios
by running large-scale simulations with thousands of agents. ACT-UP replicates
some but not all of ACT-R’s declarative and procedural memory systems.
More recently, Gonzalez and Lebiere (2005), Lebiere et al. (2009), Reitter and
Lebiere (2010), and Juvina et al. (2011) have used cognitive architectures to model
human decision making in collaborative tasks. While our work builds upon these
efforts, our interest is how cognitive and environmental factors, modify network
formation and structure.
There is a rich literature on how proximity influences social ties. We note a few
examples. Kraut et al. (2002) found that actor proximity fundamentally influences
the evolution of network topologies by determining the interaction frequencies of
actors across the network, while Allen (1984) demonstrated that the probability of
two people communicating in an environment could be represented with a
decreasing hyperbolic function of their distance. Beyond a certain distance, the
probability that two people will communicate decreases rapidly, making tie
formation unlikely (Carley 1991, 1992). This work suggests it is useful to examine
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how cognitive and environmental factors interact to condition interaction opportunities and consequently the growth and structure of social networks.
Creating agents based on cognitive architectures to study social phenomena has
been a useful approach and provides us the tools to examine explicitly the
interaction of memory and environment. Cognitive models attempt to represent the
processes associated with cognition, including but not limited to perception,
decision making, and learning. Most multi-agent social simulations rely on
generalizations of these processes (e.g., Axelrod and Hamilton’s (1981) tit-for-tat
strategy) to generate useful and frequently counterintuitive results. Socio-cognitive
models attempt to explore how cognition informs social interaction. In our case, we
are interested in how imperfect memory influences the structure of human
interactions.
1.2 The effect of agents’ memory and space on nodal carrying capacity
We look at the processing of social information by exploring the concept of nodal
carrying capacity, the number of alters an ego can retain in memory. To that end, we
examine how environmental factors contribute to the consolidation and retention of
social ties.
This concept is similar to Dunbar’s (1998) social brain hypothesis, where he
argues that limitations associated with the neocortex limit the number of bidirectional ties any one person can retain in memory to approximately 150 people.
Dunbar argues that maintaining stable relationships requires repeated memory
activations to identify not only one-on-one relationships but also third party
relationships (i.e., the knowledge that my friend is also friends with other actors
who I monitor). Further, he claims that the cognitive load associated with
maintaining this set of relationships in memory rises exponentially as group size
increases (Dunbar 1998, p. 63).
Based on retrospective empirical studies, Dunbar (1998, pp. 68–75) argues that
this ratio between cognitive load and group size underlies the small-world effect
observed by Milgram (1967) and others. McCarty et al. (2001) propose that humans
retain in memory a far larger number of ties (n = 291). In part, this discrepancy is
rooted in a difference in definitions. McCarty et al. (2001) definition of a social tie
requires mutual identification as opposed to Dunbar’s stricter definition of mutual
identification as well as placement in the network. In this work, the social ties we
identify are closer to McCarty et al.’s definition. Nevertheless, we believe that our
simulation is still relevant to Dunbar’s social brain hypothesis because both
concepts concern the effect of imperfect memory on the number of social ties an
individual can maintain in memory.
Consequently, in our experiments, we expect that larger populations acting over
longer time periods in fully connected environments will result in the most
connected declarative network structures. We also expect that less connected
environment layouts will result in interaction networks that consist of smaller and
more locally clustered ego-nets, resulting in more fragmented networks. We also
expect that map configurations characterized by nexus points (locations which act as
hubs by virtue of being centrally located) will exhibit behaviors similar to the water-
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Factors of interest in agent-based socio-cognitive simulations
119
cooler effect (DiFonzo 2008). We, however, are less certain where we might see
thresholds in network formation, where for instance population growth no longer
has an effect or run time is no longer relevant.
1.3 Preview of the paper
Our model is unusual in that we model social processes using a cognitive
architecture (ACT-R) that is primarily associated with cognitive science. Our model
follows in this tradition, but focuses on the effect of memory as opposed to decision
making in an attempt to explore aspects of Robin Dunbar’s (1998) social brain
hypothesis. Our emphasis is to show memory’s effect on the formation and structure
of interaction networks, not as it informs choices but as it structures interaction
opportunities. We do this in three analyses using relatively simple agents that
feature ACT-R’s Declarative Memory (DM) activation and decay function.
Analysis 1 shows the formation of networks by comparing agents using a fixedpath as opposed to a random-path navigation pattern; we find that memory in
conjunction with environmental factors predictably influences the networks’
formation rate. This rate follows the population growth sigmoid function, with
networks composed of rationally bounded agents better approximating the function.
Analysis 1 further suggests that memory is likely to influence the ultimate structure
of social networks.
We confirm this hypothesis in analysis 2 by showing the effect of memory on five
network measures, demonstrating that the useful range of variance for these
measures is contingent on memory. Finally, in analysis 3, we analyze the effects of
memory and environment on the topologies of 165,240 merged ego-nets. We found
that memory and environmental factors were all significant and that the influence of
spatial configuration on network topologies is conditioned by the joint effects of
memory and population size in some interesting ways. Based on these results, we
are able to make some suggestions for reporting work in this area.
2 Experiment environment and agents
Simulations using multiple cognitive agents need not be as onerous to design and
build as in the past. It has become easier to build cognitive models (Ritter et al.
2006). Also, with the increase in power of desktop computers, it is now possible to
run interesting network simulations locally. Preliminary explorations may be
necessary to find what factors we need to pay attention to, to record and report, and
to explore when simulating network formation and structure. This paper is a starting
point for these tasks.
All of our experiments were conducted on a 2 GHz eight-core server with 8 GB
of RAM. The server runs Linux 2.6.31 under Ubuntu 11.04, with SBCL 1.0.52 Lisp,
and ACT-R 6 (Anderson et al. 2004). Appendix 1 has further details.
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2.1 The VIPER environment
Because we are interested in the constraints associated with embodiment, and need
an environment to support multi-agent simulation with cognitive agents, we
developed the VIPER environment. It is lightweight in that it is text-based, but is
extendable and records agent behaviors. VIPER allows multiple agents to connect to
it via Telnet, and for these agents to run in real or (faster) simulated time. The
network’s speed and frequency of communication are determined by its component
agents, with no queue of events being enforced. VIPER is designed so variations in
performance originate from the agents participating in the environment, versus
being a function of the environment. The VIPER server is based on NakedMUD, an
open-source MUD environment.
Within the environment provided by the server, agents or human subjects are
situated on maps of interconnected rooms. The agents can see and communicate
with others within each room. Agents can walk between the rooms, and can interact
with objects in the rooms.
2.2 ACT-R agents
For our agents in the simulation, we built two types of ACT-R models. One
conducts random walks in the environment. The other follows a fixed path. Both
models contain two types of declarative memories: a ‘‘goal’’ type containing the
agent’s current location, remaining steps, total friends counts and a ‘‘friend’’ type
used to store friend’s names. The model consists of four basic components with nine
productions.
First, the agent’s ‘‘walking’’ component selects an available direction randomly
or from the fixed path, and sends a moving message to VIPER. Second, the
‘‘waiting’’ component utilizes ACT-R’s temporal buffer to wait 16 real-time
seconds before allowing the agent to enter a new room, to simulate transition time.
Third, the agent’s ‘‘checking’’ component, consisting of three productions, checks if
the current room is empty. Fourth and finally, the ‘‘memorizing’’ component, also
three productions, first checks DM to see if the agent has previously encountered the
agent it has just seen. If not, the model creates a new friend memory chunk, using
the imaginal buffer to store the new agent name.
Each memory chunk i is assigned an activation value Bi to represent current
retention. This activation will decay over time, and the number of active memory
chunks is influenced by several factors, including initial memory activation,
retrieval activation threshold, memory decay rate, time of retrievals, and practice
time. In Eq. 1, n represents the number of presentations associated with chunk i; d
represents the decay parameter; tj represents the time since the jth presentation.
ACT-R calculates the time since last presentation (tj) in milliseconds, and this
equation is usually used to predict memory retention for short durations (i.e., less
than 1 h). Pavlik and Anderson (2005) have extended this theory to a long-term
memory by changing the time parameters, allowing for the modeling of more
complex social phenomena.
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Factors of interest in agent-based socio-cognitive simulations
Bi ¼ ln
n
X
j¼1
tj#d
!
121
ðChunk activation based on times of usesÞ
ð1Þ
When our agents retrieve/recall a memory chunk (i) there are three parameters
involved in the recall process, the retrieval activation threshold, current activation
value, and a noise parameter (s). The retrieval activation threshold is a minimum
activation to retrieve a chunk. Equation 2 shows how the probability of recall also
depends on the current activation value (Ai) and noise parameter (s). As the
activation becomes higher or the noise parameter becomes lower, the probability of
recall is higher.
recall probabilityi ¼
1
s#Ai :
1þe s
ðThe probability of recalling a declarative memoryÞ
ð2Þ
When a chunk is successfully retrieved, there is a retrieval latency time that is
determined by the activation value. Equation 3 shows the relations between
activation value and retrieval latency time (F is a latency parameter): if the
activation value is high, it will take less time to retrieve a memory chunk. Because
activation value can be used to infer retrieval time (as shown in Eq. 3), we can
express our network semantics in terms of recall time for an alter (another agent),
which then allows future comparison to human data.
Time ¼ Fe#A
ðThe time to recall a declarative memory based on its activationÞ
ð3Þ
In our simulation, we implement each agent-to-alter relation as a DM
(Declarative Memory) chunk associated with an activation value. The result of
our simulation directly outputs a list of activation values of these relations. We use
each alter’s activation value, which allows us to infer how long it would take to
recall the alter, to identify network ties. Thus, as the activation threshold for
determining if a network tie exists increases, the semantics for identifying another
alter as an acquaintance become more and more stringent.
3 Data and methods
The VIPER environment allows many ACT-R agents to interact with each other.
These interactions produce representations of these other agents (alters, from the
point of the view of the ego), which can then be interpreted as networks. By
manipulating parameters of the simulation, we can observe changes in the growth
and final structure of the resulting networks. This process is illustrated in Fig. 1.
To better understand how memory decay and environmental factors influence
social networks, we conduct three analyses that: (a) test the influence of memory
decay on network tie formation, (b) analyze the effects of memory decay on
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C. Zhao et al.
High-level overview of our modeling process
network structure (operationalized using five network measures), and (c) test the
joint effects of memory decay and environmental factors on network structure.
3.1 Independent variables
We manipulate the following factors (activation threshold, navigation patterns,
population size, run time, and environmental configuration) to examine their effects
on the resulting networks. Table 1 shows our simulation parameters and the
independent variables tested in each of our analyses.
3.1.1 Activation threshold
To test the effects of memory decay, we manipulate activation threshold. In our first
analysis, we treat threshold as a dichotomous variable contrasting agents
implemented with a threshold of 0 to those with a threshold of -5. In analyses 2
and 3, activation threshold is a continuous variable ranging from -5 to 5. Activation
thresholds correspond to the amount of time necessary to recall a tie. We expect our
dependent variables (the rate of network formation and their structure) are
influenced by activation thresholds, and in the case of our networks are only
meaningful within a limited range essentially approximating bounded rationality.
3.1.2 Navigation patterns
In our first analysis, we examine the rate of tie formation for agents using either a
random or fixed-path navigation pattern. In the second and third analyses, we test
the strength of the effects of memory decay and environment on network structure
by testing a boundary case (agents moving randomly).
3.1.3 Population size
In our first analysis, we examine networks consisting of 40 agents. In analyses 2 and
3, we examine networks consisting of 20, 40, and 60 agents. We use a Box–
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Factors of interest in agent-based socio-cognitive simulations
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Table 1 Experimental parameters and independent variables for analyses 1–3
Independent variables
Values
Analysis 1 (4,320 networks)
Threshold
-5 or 0
Navigation patterns
Random or fixed-path
Population
40
Run time
10–500 s
Environment
Full-grid, central, hall (100, 75, 60 % of connectivity
compared to full 2D grid)
Analyses 2 and 3 (810 distinct combinations, 165,240 merged ego networks)
Threshold
-5 to 5
Navigation patterns
Random
Population
20, 40, 60
Run time
125, 250, 500 s
Environment
Full-grid, central, hall (100, 75, 60 %)
Behnken design (Kuehl 2000) to avoid extreme treatment combinations. Consequently, we transform our original population values into an ordinal scale (-1, 0,
1).1 We expect as population increases network density will decrease as agents
encounter only a fraction of the agents in the world, and of those seen remember
even fewer.
3.1.4 Length of simulation (run time)
We run our experiments for 125, 250, and 500 s in real time. Again for analyses 2
and 3, we coded these values into an ordinal variable (-1, 0, 1). We expect
increasing the run time will increase the density of the simulated networks, as the
agents will have more opportunities to form ties.
3.1.5 Environment configuration
We test three map configurations (Fig. 2). All configurations have the same number
of rooms (25). We operationalize the concept of environment configuration in two
ways. First, we treat each configuration as a categorical variable, with the hallway
map being the reference category. Second, we isolate the effect that room
connectivity has by using a measure we refer to as grid ratio. Grid ratio is simply the
number of ties between rooms present over the number of ties possible given a flat
two-dimensional world, essentially a density measure for the three maps.2
1
When using the original variables for population and run time, we find the same directionality, no
change in the standard errors or significance, and no effect on the other variables or the explained
variance. The transformed scale does increase the magnitude of the observed effects.
2
We include both measures because they are not equivalent. We did find instances where our categorical
variable (Room Map) was significant when Grid Ratio by itself was not and vice versa.
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Fig. 2 a 5 by 5 grid map, b central area map, c and hallway grid map
The first configuration (2a) is a full 5 9 5 map with a grid ratio 1.0. This
configuration simulates an open space without spatial constraint. The second
configuration (2b) has a central area with grid ratio 0.75. This configuration
simulates an open space with some spatial constraint (e.g., a warehouse). We
believe this central meeting point will lead to network densities and clustering that
are less pronounced than those associated with the 5 9 5 map but more than those
associated with the hallway map. The third configuration (2c), our reference setting,
is a two-hallway configuration with grid ratio 0.6. This is a realistic configuration
that simulates spatial layout of a building floor with a hallway. This configuration
should lead to lower connectivity due to the larger distances between agents.
3.2 Constructing the data: showing growth and finding structure
Because we are interested in the effects of memory and environmental factors on
both network formation and their ultimate structure, we ran an initial analysis
testing our hypothesis that memory and environment influence network formation.
Drawing the growth curves of the activation networks requires taking numerous
samples at different cut points. Consequently, our first analysis uses a smaller data
set. The results of this analysis informed the design of analyses 2 and 3, where we
examine the strength of these effects on 165,240 merged ego-nets.
3.2.1 Analysis 1
Analysis 1 compares the growth curves of 4,320 activation networks. In this
experiment, we use a sample population size of 40 and a running time of 500 s. To
draw the growth curve, we collected network data at 18 time points, ranging from 10
to 500 s. We chose 500 s as the longest running time because we did not observe
any significant changes in the network after 500 s. Based on our computational
resources, each experiment setting was run 20 times. As we focus on the growth
pattern of social networks in this experiment, the time parameters are not directly
applicable. However, Pavlik and Anderson’s (2005) results suggest that we can
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Factors of interest in agent-based socio-cognitive simulations
125
generalize the results of our short-term simulations to larger time scales because
ACT-R allows us to predict long term memory effects by applying different time
parameters.
3.2.2 Analyses 2 and 3
Analysis 2 examines changes in our five network measures as a function of
activation threshold. Analysis 3 consists of a set of Ordinary Least Squares (OLS)
regressions.3 We are confident that OLS is sufficient for our purposes because our
experimental design makes heteroskedasticity issues associated with auto regression
or autocorrelation unlikely, ensures that we can consider our independent variables
fixed over repeated samples, and eliminates the possibility of perfect collinearity.
Figure 3 shows an example ego network. We capture the effect of environmental
factors and memory constraints on network structure by combining and analyzing egonets generated by the ACT-R agents in VIPER. Each agent represents other agents it
has met as declarative memory (DM) chunks. The activation of each DM chunk can be
used to derive the probability of retrieving a chunk and the amount of time required to
recall a tie. The semantics of each dyadic tie is important in interpreting a network. An
activation value of -3 indicates that the actor will need approximately 200 ms to
recall the chunk (if they can retrieve it at all), whereas an activation of 3 indicates that
the actor will need less than 5 ms to recall the chunk (but longer to report it because of
additional processes including planning an utterance and speaking). These semantics
seem to be useful in considering social networks; if an agent cannot recall another
agent at all, it is unlikely they have a social tie.
These ego networks thus can be considered analogous to network survey data,
with a survey instrument used to gather each individual’s view on their social
network. We merge these ego files to create merged ego networks. We have two
distinct strategies for merging these ego files; we call these methods symmetricnecessary and directed-sufficient.
To merge our ego-nets, we considered two rules for determining whether a tie
exists: symmetric-necessary (where threshold, t, must be met by both Aij and Aji)
and directed-sufficient (where threshold, t, must be met by either Aij or Aji). In either
case, a binary two-way tie is formed if the necessary conditions are met. We chose
to form binary two-way ties to ensure that the network measures being used could
be compared directly. The directed-sufficient network merge method is less
conservative; typically creating more ties, differences between the networks
generated by each method may also offer interesting insights on the ramifications of
environmental structure. The semantics implied by the symmetric-necessary merge
method closely resembles Dunbar’s (1998) and McCarty et al’s (2001) mutual
identification criteria for a social tie.
For simplicity in the remainder of the paper, we will refer to the symmetricnecessary semantic as ‘symmetric’, and the directed-sufficient semantic as
3
In our analyses, we ran Cooks D and DFFITS tests. We tested our model on the entire data and
subsections of the data. The models effects were stable and we saw no evidence of problems associated
with emergence.
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Fig. 3 An example ego network, ties are colored by activation value
‘directed’. Note that all networks produced by either method are both binary and
undirected.
Given that our alter DM chunks were inherently weighted by activation value, it
was tempting to simply use the activation values to inform a weighted network
measure analysis. We chose not to do that for three reasons. Firstly, we consider that
changes to the threshold value change the meaning of the network, which makes
such a network analysis problematic. Secondly, ACT-R’s activation values range
from negative to positive values, spanning zero (0). Zero is usually reserved in
network analysis for the absence of a tie. Transforming the data is possible, for
example, by converting the activation value into the time to recall or probability of
recall but adds an additional processing step. Finally, network measures are
sensitive to the edge weighting and may produce non-intuitive results—many
network analysis tools automatically binarize networks before calculating measures.
Consequently, we used the social tie threshold to filter ego networks and infer
binarized undirected ties.
For each simulation run, we created both a symmetric-necessary and directionalsufficient network using social tie thresholds between 5 and -5, with intervals of
0.1. Thus, we created two networks per run for each tie threshold value of -5.0,
-4.9, -4.8, -4.7, and so on to 5.0. This process created a corpus of (810 runs 9 2
merge methods 9 102 threshold values) 165,240 merged ego-networks. We
included isolates, egos with no connections, in our networks.
Figure 4 offers an example of how a single merged ego-network can reveal the
strong ties in a network as the criteria for inclusion in that network becomes stricter.
By stricter, we mean that the activation threshold necessary to be considered a tie
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Factors of interest in agent-based socio-cognitive simulations
127
Fig. 4 The same ego network at various memory thresholds, a -3.5, b 0.0, and c 1.0
increases. While the three networks shown in Fig. 4 arise from the same declarative
representation, these networks reflect activation thresholds of -3.5, 0.0, and 1.0,
corresponding to networks a, b, and c respectively. In essence, network c identifies
the agent’s core relationships, those of which the agent has the strongest memory.
3.3 Formation rates and network measures: our dependent variables
and descriptive statistics
In our first experiment, we analyze changes in network tie formation rates to test the
effects of memory decay, navigation pattern, and map configuration. In our
subsequent analyses, we examine changes in five network-level measures (density,
average distance, clustering coefficient, average eigenvector centrality, and average
betweenness) to test the effects of cognitive limitations and environmental factors.
We define these measures now.
Network tie formation rate is the slope of our networks’ growth curves. The
curves show the number of ties in memory as a function of time, threshold, and
navigation pattern.
Density is the number of ties present in the network compared to the maximum
number of possible ties, excluding self-loops (Kephart 1950). Network density is a
fundamental measure of a network, with implications for the interpretation of many
other measures. Networks tend to be less dense as the population grows, but should
be denser, other factors held equal, as the simulation run-time increases (at least
until activation equilibrium is achieved for networks with memory decay).
Average distance is the number of jumps required, on average, for each agent to
reach every other agent (Moreno and Jennings 1938; Wasserman and Faust 1994). If
every agent is connected to every other agent (a density of 1) then average distance
will also be 1. Thus, dense networks tend to have average distance near 1. In ORA
(Carley et al. 2012) isolated nodes report a distance of 0 to every other agent, which
can complicate the interpretation of this measure. Thus, networks with isolated
nodes will have their average brought down towards 0.
Clustering coefficient is a transformation, over all agents, of each ego’s local
network density, of each ego’s alters, how many of those alters are themselves
connected (Freeman 1978–1979). A high clustering coefficient in a social network
suggests a decentralized information structure and one where actors tend to have an
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Table 2 Descriptive statistics for symmetric and directed networks (Analyses 2 and 3)
Dependent variable
Mean
SD
Median
Interquartile range
Range
Symmetric networks (n = 82,620)
Density
0.34
0.38
0.07
0–0.85
0–1
Average distance
0.68
0.73
1
0–0.02
0–6.68
Clustering coefficient
0.43
0.43
0.34
0–0.93
0–1
Eigenvector centrality
0.07
0.16
0.02
0–0.06
0–1
Average betweenness
0.01
0.04
0
0–0.001
0–0.76
Directed networks (n = 82,620)
Density
0.42
0.41
0.5
0–0.86
0–1
Average distance
0.65
0.59
1
0–0.01
0–5.54
Clustering coefficient
0.5
0.46
0.83
0–0.94
0–1
Eigenvector centrality
0.04
0.13
0.017
0–0.017
0–1
Average betweenness
0.01
0.06
0
0–0.0004
0.89
accurate understanding of the state of their local work-group. This measure is highly
correlated with density.
Average network eigenvector centrality is a measure of the second-order
connections an agent has (Bonacich 1972). Because eigenvector is normalized
against the sum of each agent’s second-order connections, density and eigenvector
interact. In very dense networks, average eigenvector is very low, typically near 0.
In very sparse networks with isolated nodes, the eigenvector will again be near 0. In
medium density networks, the eigenvector may be large. Thus, eigenvector values
tend to make an inverse U-shaped curve as network connectivity increases.
Average betweenness is a measure of a node’s prominence on the paths between
other agents (Everett and Borgatti 2005; Freeman 1978–1979). We expect map
topology will strongly affect this measure. We expect that betweenness will be
higher in environments with the hallway configuration. Betweenness is low on
highly dense networks, and also tends towards 0 in highly sparse networks with
isolated nodes.4 Betweenness, thus, also tends to have an inverse U-Shaped curve in
relation to threshold.
Table 2 shows the descriptive statistics of our five network measures for all the
merged ego-nets, symmetric and directed. We see that the median of density for our
symmetric networks are generally smaller than those in the directed networks, as
this is the more conservative method. Medians are a more useful referent as means
are vulnerable to outliers.
4 Results
This section presents the results of our three analyses. Our first analysis examines
the effect of memory decay, map configurations, and navigation patterns on the
4
In ORA, the treatment of isolated nodes for path-based measures is customizable. We use a simple
default where nodes report a ‘0’ to nodes they cannot reach.
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Factors of interest in agent-based socio-cognitive simulations
129
formation of networks. We next examine five network measures as a function of
activation threshold. Finally, we examine OLS regression results to better
understand the joint effects of memory decay and environmental factors.
4.1 Threshold’s effect on network formation
Analysis 1 shows the effects of the model’s three parameters on the rate of tie
formation. Based on these figures, we will discuss how memory thresholds, map
configurations, and navigation patterns influence the formation rates of simulated
networks.
Figure 5 shows the growth curve of a network consisting of agents using the
fixed-path navigation pattern within the Hallway map. The x-axis represents
simulation time in real seconds, the y-axis the number of ties in memory. The solid
line with open triangles represents the network formation rate of a network where no
memory threshold was applied—if an agent met an agent, they formed a permanent
tie (the directed-sufficient method). We find that the upper curve increases rapidly
and then flattens when it reaches 1,336 ties (the maximum is 40 9 39, or 1,560, if
the agents’ paths completely overlap, which they do not).
The line with filled triangles in Fig. 5 represents the network formation rate of a
network where a memory activation threshold of 0.0 was applied. According to the
ACT-R theory, the activation threshold represents a memory limitation, meaning that
memory chunks with an activation value lower than the threshold cannot be retrieved.
The top curve’s more gradual progression illustrates the influence of memory on the
formation rate: multiple exposures are required to remember another agent, while the
difference in total number of ties (800 versus 1,336) illustrates memory’s effect on the
network’s density. In addition, this network never achieves a fully connected state, in
the sense that the agent’s declarative representation at no point includes the total set of
possible interactions. In other words, these agents must continue to maintain their
relationships because they continue to forget. Nevertheless, this network does
eventually achieve equilibrium, with agents forgetting old alters as quickly as they
meet new ones, around 150 s with a network tie count of 800 ties.
Fig. 5 The effect of memory threshold on network formation over time for the fixed path navigation
pattern in the hallway map (n = 40)
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Comparing the two curves in the Fig. 5, we notice another difference, the time at
which the rate of growth begins to increase. For the thresholded network, this time
happens later than for the un-thresholded network. This is because tie formation for
thresholded agents requires multiple exposures. Initially, agents are busy simply
encountering other agents and building their friends list. As they, however, begin to
meet more ‘‘old friends’’, the activation values of friendships start to increase
enough to be retrieved.
We set the travel interval between rooms at 16 s to make the effect of memory
decay more prominent. Nevertheless, we recognize this interval is unrealistic
because people can take minutes or hours to find one another. As this work only
focuses on the growth pattern of social networks, however, we argue that the
measurement of time is a secondary factor in this case because over 80 % of the
decay happens in the first 16 s according to ACT-R’s decay function, with little
additional decay occurring at greater time scales. In exploratory tests, we found this
to be true, resulting in our choice of a total running time of 500 s and a travel
interval of 16 s.
Figure 6 shows the growth curve of a network of agents moving through the
Hallway map using the random navigation pattern. Comparing Figs. 5 and 6, the
non-threshold curves have the same growth pattern, but the threshold curves appear
to be different. Memory appears to have different effects based on the setting and
navigation pattern in which the agents operate.
Figure 7 compares the growth curves of two networks where a memory retrieval
threshold of 0.0 was applied; these networks differ with respect to the navigation
pattern used by the agents. The fixed path-pattern (dashed line) forms ties more quickly
than the random-path pattern. We suspect that the fixed-path pattern achieves
equilibrium sooner because it is more localized, and thus provides more chances for
agents to meet their ‘‘old friends’’. On the other hand, both networks achieve
equilibrium at about 800 ties, suggesting that the navigation patterns in this simulation
do not constrain the total number of relations an agent can maintain in memory.
Figure 8 compares the network formation rates of networks occurring in each of
the three map configurations (full grid, central, and hallway); all these networks
consist of agents with a memory activation threshold of 0.0. We find that the map
configurations have a similar influence on the networks’ growth curves as the
navigation patterns. Again, the map configurations influence the rate of formation
but not the network’s density at equilibrium.
In Fig. 8 the Hallway map (grid ratio = 60 %) is associated with the longest
delay in network formation and the lowest rate of increase; the full grid map (grid
ratio = 100 %) has the shortest delay and the fastest rate of tie formation. These
results show that delay in the network’s growth rate is negatively correlated with
map configuration (operationalized as grid ratio), while the network’s growth rate
during its growth spurt is positively correlated.
Besides the threshold effect, we also find that the networks’ formation rate
follows a logistic equation. As Verhulst (1845) showed in his article, Mathematical
Researches into the Law of Population Growth, population growth follows a
sigmoid function. His equation models population growth as a three-step process,
(1) firstly, the population has a delay step when a new species is adjusting to the
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Factors of interest in agent-based socio-cognitive simulations
131
Fig. 6 The effect of memory threshold on network formation over time for the random walk pattern in
the hallway map (n = 40)
Fig. 7 The effect of navigation pattern on network formation over time in the hallway map with
threshold (n = 40) for agents with a memory threshold
environment; (2) secondly, the species populates exponentially when they have
adapted to the environment; and (3) thirdly, the population size reaches an upper
boundary due to limits in living space and food. Figure 9 shows Verhulst’s logistic
growth curve using Pearl and Reed’s (1920) more familiar notation.
Comparing Figs. 8 and 9, we find that the network tie formation rate matches
nicely Verhulst’s logistic equation with its three phases. Based on their similarity,
we could mathematically model the formation rate by a differential logistic
equation. Equation 4 provides an approximate model of our result, in which N
represents the total number of ties, t represents time, r represents a growth
parameter, K represents the upper network capacity. This equation suggests that the
tie count and its rate of growth are related to the current network’s density and is
constrained by available cognitive capacity.
!
"
dN
K#N
¼ rN
ð4Þ
dt
K
ðThe differential equation represents network growth patternÞ
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Fig. 8 The effect of map configuration on network formation over time (n = 40) for the random walk
agent
Fig. 9 Population growth as a function of species population and living time
4.2 Network structure as a function of threshold
Analysis 2 shows the effect that tie threshold has on the aggregate characteristics of
the symmetric networks and directed networks from the final state of the simulation.
Analysis 1, which shows how the networks grew over time, is suggestive in several
ways. One, it shows that thresholded networks exhibit fewer ties and thus lower
functional densities. Two, it shows that map configurations and locality are
important, at least on the rate of tie formation. On the other hand from these
analyses, we can make a few inferences about the effect of memory decay on
network structure. Analysis 1 shows the maximum connectivity associated with two
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Factors of interest in agent-based socio-cognitive simulations
133
threshold conditions; and it shows the time required to reach that maximum as a
function of two factors (room configuration and navigation patterns). From analysis
1, however, we cannot ascertain the effect memory decay has on network structure,
other than to speculate about its effect on density.
Figure 10 presents ten plots that display the changes in five network measures as
a function of tie threshold (the definition of what constitutes a social tie based on the
length of time to recall an alter). Each plot has three lines: each is the mean for each
of the three population values. The dot–dashed green line is population 20, the
dashed red line is population 40, and the solid blue line is population 60. Highly
translucent scatter points, similarly colored, are included to give an indication of
spread for the measure as a function of threshold.
The plots show that, as the memory threshold increases from -5 to 5, that all
measures change significantly, especially when threshold values range between -1
and 1.5. We see this as the cognitive band (Newell 1990, p. 7). It corresponds to
time retrieval for the chunks as ranging from 28 to 2 ms for retrieval of the alterchunk, based on our setting for the noise parameter (s) of -3.5. Measures at
thresholds outside this range effectively represent hypothetical boundaries of
perfect memory when the retrieval threshold is below -1 and non-existent
memory above 1.5. Thus, Fig. 10 suggests that the applicability of these measures
(the range of meaningful variance) to social networks relies, in part, on the
bounded rationality of their nodes. Comparing the directed and symmetric
networks, we see that symmetric networks have less variance as threshold changes.
This difference is an artifact of the stricter reciprocity criteria associated with the
symmetric networks.
We also find that the threshold, within our found cognitive bounds, has a positive
influence on average distance, average eigenvector centrality, and betweenness,
while having a negative influence on density and clustering coefficient. This result
implies that when increasing activation threshold, the overall density of the network
will shrink but the network will split into several smaller and tighter groups with
more second-order connections, as can be seen previously in Fig. 4.
4.3 The effects of threshold and environment on network structure
Analysis 3 shows regression results for each measure, with y being a function of
threshold, running time, population, room map, grid ratio, and threshold2 (squared
threshold). Equation 4, the equation for clustering coefficient, is an example. Based
on the results of analysis 2, we focus our analysis on predicting each measure when
threshold is between -1 and 1.5.5 We included threshold2 because we found
threshold has the largest regression parameters and the relation between threshold
and all measures is apparently non-linear (see Fig. 10).
5
In ORA, the treatment of isolated nodes for path-based measures is customizable. We use a simple
default where nodes report a ‘0’ to nodes they cannot reach.
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Fig. 10 The distribution of each network measure as a function of threshold for both symmetric and
directed networks. Translucent scatter points, similarly colored, give an indication of spread for each
measure
Clustering Coefficient
¼ 0:67 þ #:40ðThresholdÞ þ :23ðRun TimeÞ þ :12ðPopulationÞ
þ 0:3ðRoom MapÞ þ :12ðGrid RatioÞ þ #:09ðThreshold2 Þ þ e
ð4Þ
ðEquation for clustering coefficient for directed networkÞ
We then analyze regression results by population size, identifying instances where
environmental configuration is more or less important. Analysis 2 established that
threshold has an effect on network structure; analysis 1 showed that environmental
factors, at a minimum, influence the rate of tie formation. Brantingham and
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Factors of interest in agent-based socio-cognitive simulations
135
Fig. 11 a Hallway map’s heatmap; b Agents-by-location network
Brantingham (1993) found that environment configurations create loci of interaction or
activity spaces. These locations are where the majority of interactions occur.
Brantingham and Brantingham use this concept to study crime densities, but this idea
can be expanded to other activities, such as co-occurrence or socialization. From this
research, it seems reasonable to conclude that environment configurations have
implications for the structure of agents’ friend networks as well as their formation rates.
Analysis 1 lends support to this argument. Figure 11a shows a heat map of
relative room activity in analysis 1 for the hallway configuration, while Fig. 11b
shows the connectivity between all agents and the rooms in which they interacted.
The concentration and degree of these spaces suggests that agents who travel
between activity spaces tend to travel along the same path, creating more interaction
opportunities. Consequently, we theorize that the effect of room maps and grid ratio
are influenced by population size.
4.3.1 Comparing symmetric and directed networks
We next compare the symmetric and directed networks. Table 3 shows the parameter
coefficients of each of our measures for the symmetric networks. We see that our
model best explains the variance associated with density, average distance, and the
networks’ clustering coefficient, while explaining less well changes in eigenvector
centrality and betweenness. As these latter measures generally exhibit an inverse
U-shaped curve as networks move from highly dense to sparse—this is not surprising.
We see for each dependent measure that the effect of threshold and threshold2
are significant, although the directionality with respect to each other is not always
consistent. These effects generally exhibit the largest magnitude. We, however,
must be cautious in comparing relative magnitudes due to the fact that room map
and grid ratio are collinear. As analysis 1 predicted, we find that as threshold
increases density decreases, essentially as agents forget alters they are less able to
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Table 3
C. Zhao et al.
Symmetric network measure comparison (n = 82,620 networks)
Independent
variables
Density
Average
distance
Clustering
coefficient
Eigenvector
centrality
Betweenness
Threshold
-0.30*** (0.00)
-0.52*** (0.01)
-0.41*** (0.00)
0.05*** (0.00)
-0.03*** (0.00)
Run time
0.06*** (0.00)
0.50*** (0.01)
0.11*** (0.00)
0.07*** (0.00)
0.02*** (0.00)
Population
-0.05*** (0.00)
0.06*** (0.00)
-0.04*** (0.00)
n.s.
-0.02*** (0.00)
Room map
0.03*** (0.01)
n.s.
0.05*** (0.01)
n.s.
n.s.
Grid ratio
0.16*** (0.03)
n.s.
0.24*** (0.04)
n.s.
n.s.
Threshold2
0.17*** (0.00)
-0.67*** (0.01)
0.13*** (0.00)
-0.24*** (0.00)
-0.02*** (0.00)
Intercept
0.02
1.39***
0.1
0.43***
0.09**
Adjusted R2
0.76
0.54
0.79
0.22
0.24
-55,460.828
-105,449.55
BIC
-12,634.49
-12,634.49
-76,865.20
Standard errors are in parentheses. n.s. indicates not significant values
* p \ 0.05, ** p \ 0.01, *** p \ 0.001
capitalize upon all the possible ties in the set. We also see that average distance,
clustering coefficient, and betweenness decrease while network eigenvector
centrality increases, which lends support to our interpretation in analysis 2 that as
threshold increases more subgroups with more second-order connections form.
We see for every unit increase in run time a corresponding increase in density,
average distance, clustering coefficient, eigenvector centrality, and betweenness,
suggesting as indicated by analysis 1 that by 500 s the networks in memory have
achieved a stable pattern. We also see that an increase in population, as expected, leads
to a decrease in density and clustering coefficient, as these two measures are highly
related. The decrease in betweenness combined with the increase in average distance
suggests that as the population increases the network as a whole tends to fragment.
Interestingly for symmetric networks, population’s effect on eigenvector centrality is
insignificant, this may be a result of reciprocity criteria combined with the random
movement pattern. Essentially, no group leaders form, when we require agents to
acknowledge the tie, because the agents are moving randomly through the environment.
Finally, we find the effects of room map and grid ratio to only be significant for
network density and clustering coefficient. We find that as grid ratio increases or as
room map changes (from Hallway to Central and Grid configurations), density and
clustering coefficient also increase. Although these measures are collinear, they are
not perfectly so; and we found that separating them improved the overall fit of the
model. As our heat map analysis suggested (Fig. 11), the influence of room map and
grid ratio seems, in part, a function of population. As these two measures are the
most directly affected by shifts in population, they are also the most likely to be
sensitive to shifts in room map and grid ratio.
Table 4 shows the parameter coefficients of each of our measures for the directed
networks. The results are similar but not identical. We find that threshold and
threshold2 are significant and in the same direction as in the symmetric networks;
however as suggested in analysis 2, the directed networks appear more linear, as the
magnitude of threshold2 is far less. Run time also remains significant but moves in
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Factors of interest in agent-based socio-cognitive simulations
Table 4
137
Directed network measure comparison (n = 82,620 networks)
Independent
variable
Density
Average
distance
Clustering
coefficient
Eigenvector
centrality
Betweenness
Threshold
-0.35*** (0.00)
-0.15*** (0.01)
-0.40*** (0.00)
0.09*** (0.00)
0.01*** (0.00)
Run time
0.21*** (0.00)
0.17*** (0.00)
0.23*** (0.00)
-0.04*** (0.00)
-0.01*** (0.00)
Population
-0.13*** (0.00)
0.12*** (0.00)
-0.07*** (0.00)
0.05*** (0.00)
n.s.
Room map*
n.s.
n.s.
0.03* (0.01)
n.s.
n.s.
Grid ratio
n.s.
n.s.
0.12* (0.06)
n.s.
n.s.
Threshold2
-0.05*** (0.01)
-0.41*** (0.01)
-0.09*** (0.00)
-0.08*** (0.00)
-0.03*** (0.00)
Intercept
0.72***
1.07***
0.67***
0.05
0.04
Adjusted R2
0.77
0.29
0.77
0.09
0.04
BIC
-65,998.0
-24,340.0
-62,330.6
-56,519.1
-93,633.7
Standard errors are in parentheses. n.s. indicates not significant values
*
The hallway map is the reference category for this and the subsequent analysis
* p \ 0.05, ** p \ 0.01, *** p \ 0.001, *** p \ 0.001
the opposite direction in the cases of eigenvector centrality and betweenness. We
suspect this difference is due to the time requirements of our symmetric-network
merge method, where more time is required to meet the reciprocity requirement.
Population’s significance and directionality are the same for the networks’ density,
average distance, and clustering coefficient; however, we see a significant positive
effect for eigenvector centrality and no effect for betweenness while we see the opposite
trends in the symmetric networks (no effect on eigenvector centrality and significant
negative effect on betweenness). We suspect that the opposite trends in directed and
symmetric networks with regards to eigenvector is the result from the difference in tie
criteria. Directed networks that require only a single nomination to establish a tie feature
more unique agent-to-alter relations. Because eignvector centrality approaches zero as
networks shift from being dense to very dense, we suspect the difference in population’s
main effect in these two setting can be explained as a difference in the effect of an
increase in population on moderately dense network compared to a very dense network.
With regards to betweenness, the directed networks tie requirements allow for the
retention of more ties, meaning more paths between the agents. The increase in paths
has a suppressive effect on betweenness as seen in the symmetric networks; but in the
directed networks, high density is almost assured, limiting the amount of meaningful
variation in the betweenness measure.
With regards to room map and grid ratio, we see the effects of these two factors
are in the same direction for the networks’ average clustering coefficient but are less
significant. For directed networks, they have no effect on density. Again, this
difference is likely a result of the more relaxed tie requirements—the lack of a
reciprocity criteria means that agents’ require fewer interactions to establish a tie.
4.3.2 The effect of environment in relation to population size
Our heat map and co-occurrence network analysis suggests that population size was
likely to influence the degree to which environmental configuration (operationalized
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Table 5 Environmental effects as a function of population
Measure
Population 20
Population 40
Population 60
Symmetric networks
Density
Room map (2)
Room map (1)
Room map (2)
Grid ratio (?)
Grid ratio (1)
Grid ratio (2)
Average distance
Clustering coefficient
Eigenvector centrality
Room map (2)
Room map (1)
Grid ratio (?)
Grid ratio (1)
Room map (2)
Room map (1)
Grid ratio (2)
Grid ratio (1)
Betweenness
Directed networks
Density
Room map (1)
Room map (2)
Grid ratio (1)
Grid ratio (2)
Average distance
Room map (2)
Grid ratio (2)
Clustering coefficient
Room map (1)
Grid ratio (1)
Eigenvector centrality
Betweenness
Room map (1)
Room map (1)
Room map (2)
Grid ratio (1)
Grid ratio (1)
Grid ratio (2)
Signs indicate the directionality of the relationship, Blank cells indicate non-significant effects
as room map and grid ratio) influences our measures. Table 5, a summary of six
regression analyses found in Appendix 2, supports this conjecture.
Table 5 shows that environmental configuration differs in significance with
respect to population. Interestingly, for both network types, environmental
configuration has a greater impact for population sizes of 20 and 60. We see,
however, that environmental configuration seems to play a greater role in symmetric
networks, where the reciprocity requires on average more interactions to form a tie.
For the directed networks, it is interesting to see that environmental configuration
affects networks consisting of 60 agents for four of the five measures. We suspect
that for these networks the comparative advantage of grid and central configurations
are at their greatest, where agents are likely to have many interaction opportunities
but also many missed opportunities.
5 Discussion and conclusions
Anderson’s Decomposition Thesis says that ‘learning on the large scale arises from
learning on the small scale (Anderson 2002, p. 87).’ In this paper, the large-scale
learning of interest is the resulting social network of these agents and the
recognition of previous interaction partners is the small scale learning process. We
examine this thesis through a multi-agent social simulation that provides a flexible
platform to examine several factors on social networks. Taking advantage of ACT-
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Factors of interest in agent-based socio-cognitive simulations
139
R’s memory mechanism, we created an egocentric view of our agents’ interaction
networks in memory by reconstructing the declarative representations used by our
agents to recall past associations. We then merged these ego-nets to create a system
wide representation of our agents’ recalled interactions.
Based on our review, we distinguished between environmental and cognitive
factors. We focused on two cognitive factors: memory activation threshold and
navigation pattern. Our environmental factors included population size, run time, and
environment configuration (Room Map and Grid Ratio). To examine these factors, we
conducted three analyses. Our experiments’ results show each of these factors impact
the growth and structure of the merged ego-networks. The first analysis focuses on the
network formation rate; that analysis suggests that activation threshold, navigation
pattern, and room map influence the resulting network formation rate.
To explore the findings of the first experiment further, we performed two
additional confirmatory experiments. We explored the effect of threshold, population, and room map on the resulting merged networks, examining these networks
based on five standard social network analysis (SNA) measures. The second
analysis (Fig. 10) shows the effect that tie threshold has on our selected SNA
measures of both symmetric and directed networks. This second analysis suggested
that cognitive bounds contribute to the meaningful variance of these measures and
offers some indication of where these bounds may be. The third analysis is a set of
OLS regressions, evaluating the utility of each of our independent variables
(threshold, population, room map, grid ratio) on each selected SNA measure, as well
as providing useful information on the directionality of these effects. One
interesting insight of Analysis 3, shown in Table 5, is that the relationship between
environmental configuration and these various SNA measures is dependent on
population, which suggests the importance of cognitive limits in that they prevent
agents from capitalizing on the full set of alters available for interaction.
These results have implications for network formation, reporting network
models, and suggest future work based on the limitations of our current work.
5.1 The implications for modeling network formation
We can view the progression of the thresholded curves depicted in Figs. 5, 6, 7, 8 as
corresponding to three stages in the formation of a network, though at abbreviated
time scales. In the simulation running 500 s, the network’s total tie count grows in
three periods: the counts remain low and unstable in the first period; it increase
rapidly in the second period; and it stops growing and remains stable in the last
period. The network tie count is stable at roughly 800 ties (an average of 20 ties per
agent). Comparing the formation curves, we see that grid ratio and navigation
pattern both impact the formation rate. Specifically, grid ratio has a positive
influence on the formation rate when agents employ a random-walk pattern. We
conclude that the grid ratio of an environment is an important factor for embodied
simulation of network formation and should be reported.
Interestingly, the growth pattern of these declarative representations seems to
correspond to the growth of populations, as both are characterized by these three
stages. Additionally, the growth of these representations has an intuitive appeal, as
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we can interpret these stages in terms of direct experience (e.g., the tendency of
people to take time to develop relationships with other people as they become more
familiar with their surroundings). This analysis suggests that it may be fruitful to
model the mediating influence of memory on network density using population
growth models when simulating disruptions to social networks (i.e., using growth
models to provide better estimates of the time required for a social network of
various sizes to acquire new ties). However, although ACT-R is nominally capable
of representing alter retrieval on appropriate time-scales, work remains to identify
an appropriate DM chunk structure for alters.
Although Analysis 1 is suggestive, in that it shows a relationship between
cognition and network density, density is only one measure. Density constrains
structure, in that there is little useful variation associated with other network
measures as networks approach maximal and minimal density. In the former case,
no node or path is uniquely privileged and thus there exists no structural advantage.
In the latter, the network is so sparse that relations, and thus the representation itself,
ceases to be meaningful. Consequently, further analyses were necessary to
understand how the interaction between cognition and environment influences the
structure of social networks.
Analyses 2 and 3 suggest that meaningful variation associated with five common
SNA measures has a cognitive foundation. For analysts conducting empirical
studies of firms or testing the resiliency of defense networks, this finding may seem
obvious and offer little traction. For the purposes of many studies, the impact of
cognition can be accounted for using a few generalizations (e.g., specifying the
number of interactions necessary to constitute a tie). Or, for institutional scholars,
this analysis may appear trivial in that it strips away the structuring influence of
institutions—there is no account of hierarchy, preferential attachment, or of social
closure.
These analyses, however, offer a powerful corrective. First, as analysts seek to
better understand multimodal and multiplex networks, we cannot assume that every
node or relation shares the same basic constraints and thus that measures have a
comprehensive meaning for the entire network. As Fig. 10 shows, networks
composed of nodes with perfect memory have different characteristics than those
operating in the cognitive band; and as Tables 3, 4, and 5 show the effects of the
environment on these network measures may be nuanced and multi-faceted. We saw
these effects even in a simulation where agents move randomly and social
interaction was limited merely to remembering previous interaction partners, there
is no reason to expect this would not hold true in simulations with richer agent
representations and interaction opportunities. In short, you cannot remove the social
context from the interpretation of a social network measure. So, we conclude that
network simulation of cognitive agents need to include the effect of memory or risk
not making accurate predictions of human network structure.
Another implication of this work is that agents that co-locate do not always know
each other. This supports Cranshaw et al.’s work (2012) on what they refer to as
‘‘livehoods’’. We conclude from this analysis that other analyses that that assume
co-location to infer ties are using a problematic assumption. Agents may collocate
based on other factors than knowing each other, even repeated collocations. For
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Factors of interest in agent-based socio-cognitive simulations
141
example, not all students in a class know each other. And if collocated and they
have met, they will not always remember that.
5.2 The implication for reporting network studies
Finally, these analyses suggest that our selection of our tie criteria is important and
influences our results. Unlike common social tie criteria, such as interaction count,
the criteria we used here, based on activation threshold, has important homeostatic
properties implicit in a cognitive architecture, which suggests that time is important
in the interpretation of a human’s social network. Criteria such as interaction count
result in network formations that are persistent and aggregative over time, resulting
frequently in what are called scale-free structures. Although it is infeasible to derive
directly a cognitive activation value for humans interacting with other humans,
using an algorithm for determining ties that is sensitive to the timing of the
interaction events seems like it would produce networks more similar in structure to
human networks in our minds, which we believe is sympathetic to the approach
discussed in Anderson and Schooler (1991). This limitation of traditional tie criteria
may be partially ameliorated through accounting of time in the sampling process
(e.g., latent growth modeling) or by using a specific time window (e.g., Cranshaw
et al. 2012).
These findings suggest that future simulations examining generative social
networks must control and carefully report particularly criteria, memory quality, and
running time. All have an effect on networks and network formation.
5.3 Implications for cognitive science
The time-scales for memory retrieval of these chunks suggest that the cognitive
band in our data appears to be important for social agents. As our cognitive agents
become more complex and have social ties, the information about human social ties
can provide an additional constraint on our cognitive theories.
This work extends Morgan et al.’s (2010) work examining the influence of
environmental factors on cognition and social interaction. Cognitive theories
generally limit the influence of environment to inputs in the decision cycle. State
changes in these models are the result of previous actions. Our work suggests that
environmental factors influence interactions at a more basic level through relational
networks in the mind. As cognitive theories move from modeling actions occurring
at the cognitive and rational bands to the social band, we will need to formalize our
understanding of the persistent effects of environment on memory. Simply put,
modeling long term collaborations or social learning will require more than
refreshing our agents’ initial friends list. Although ACT-R is capable of representing
alter retrieval on appropriate time-scales, work remains to identify an appropriate
DM chunk structure for alters.
Table 5 suggests that even for these simple agents we can see the effects of
limited attention as the population increases, indicated by the shift in the effect of
grid ratio on density as the population moves from 40 to 60 agents. In our model, we
identified core friend groups using memory thresholds after the fact; however,
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C. Zhao et al.
modeling long term collaborations will require more explicit models for recalling
primary groups or significant others because agents will have to span primary
groups (recall close friends who are geo-spatially separated from them) as the
environment increases in complexity.
Humans often recall friends by recalling institutions or settings. This suggests we
need a more explicit theory of reification and schema building that accounts for the
emergence of social objects in memory. Georgeon et al. (2010) and Georgeon and
Marshall (2013) provide insights into this problem in their work examining sense
making; however, further work is necessary to extend these theories to model the
emergence of social objects and schemas.
5.4 Limitations and future work
Future research will build upon some of the more interesting issues raised by this
work. First, we would look to see if normalized thresholds have consistent effects on
network topology independent of the environment. Second, we should include more
agents and more runs (Reitter and Lebiere 2011), as we examined only a small set of
factors and environmental configurations.
Second, our claim to ‘‘cognitive agents’’ is somewhat weak because it rests
nearly exclusively on the memory decay function. Our agents do not use many
aspects of the ACT-R architecture, for example, perceptions do not inform
decisions, perceiving a ‘‘friend’’ does not inform whether the agent decides to go to
another room (i.e., our agents never choose to hang-out), and the agents do not have
extensive knowledge. Extending the agents to interact more with the world and to
have their behavior influenced by more sophisticated knowledge structures are
obvious places for future work. For instance, such models would help to explore the
influence of small cognitive effects (such as memory slips or motor control errors)
on information diffusion or collaboration.
Finally, we would extend our analysis to see if Dunbar’s Number arises from
agents managing social ties while completing essential collaborative tasks (e.g.,
foraging for food). Testing this hypothesis will require increasing the population
size and incorporating a task model, among other things.
Acknowledgments This work was supported by a grant from DTRA (HDTRA1-09-1-0054). We thank
Jaeyhon Paik for help on the agent design and Jeremy Lothian for assistance with VIPER.
Appendix 1: Simulation implementation details
To connect ACT-R to VIPER, we implemented the Telnet Agent Wrapper for ACTR (TAWA) in Common Lisp. It supports logging in, waiting for synchronization,
logging, halting, and writing results to CSV files. It also exports a number of
functions that provide ways to examine the environment, speak, listen, move, and
otherwise control a virtual body in VIPER.
When an ACT-R model is wrapped by TAWA, executions of model code are
delayed until a privileged administrator agent signals for synchronization. Error
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Factors of interest in agent-based socio-cognitive simulations
143
conditions are also caught by TAWA and standard UNIX error codes are returned
instead of dropping into the more standard debugger. For example, a successful run
returns 0 to the parent process, while any error (e.g., network errors like the server
being unreachable) returns a non-zero value. Returning error codes like this allows
automated error checking in large-scale experiments.
Because memory decay and networks are strongly temporal, we paid special
attention to time. To synchronize the agents, the administrator agent (which does
not take part in the experiment) waits for all of the TAWA wrapped agents to finish
loading and logging in. It then signals to TAWA to begin the simulation. Because
TAWA delays the evaluation of the model code until synchronization, no agent
experiences time before the synchronization signal. Further, all ACT-R models are
set to run in real-time and for the same amount of ‘‘real-time’’, so they all halt after
the same perceived period. Thus, the total time experienced is the same for all
agents.
Early benchmarks showed that ACT-R processes took up about 80 MB per
process. We would only have been able to run about 100 processes on a single 8 GB
machine before swapping would occur. To reduce the per-process footprint, a
number of optimizations were implemented. Basic space reductions were achieved
by using the DECLARE Lisp construct, as well as by pre-compiling the
components, removing the debugger, and saving the whole system (sans the
ACT-R agent model) as a system image. This reduced our per-process memory
footprint somewhat, but they were not the biggest contributions towards memory
usage reduction.
In SBCL Lisp 1.0.52, the ‘‘–merge-core-pages’’ flag was recently added. This
flag enables Kernel Same Page Merging under recent versions of Linux (Arcangeli
et al. 2009). This optimization flags shared areas of memory as being able to be
merged unless modified. Because a significant percentage of our agents were
replicated, we found that we could reduce the per-process memory footprint as low
as 8 MB per process (with one shared copy of the merged pages excepted). Thus,
the only activities that increase the size of this footprint are changes within
individual agent models. Sharing and merging copies increases the number of agents
capable, whether on single processors or HPC. Together, these optimizations permit
orders of magnitude more agents to be run in a single experiment than many
previous efforts, enabling larger-scale analysis than has been previously done. Such
large-scale work is planned for future research.
Appendix 2: Analysis by population
Symmetric ties
Population: 20 agents
See Table 6.
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Table 6
C. Zhao et al.
Symmetric network measure comparison (20 agents)
Independent
variable
Density
Average
distance
Clustering
coefficient
Eigenvector
centrality
Betweenness
Threshold
-0.38*** (0.00)
-0.65*** (0.01)
-0.47*** (0.00)
0.07*** (0.01)
-0.06*** (0.00)
Running
length
0.06*** (0.00)
0.30*** (0.01)
0.07*** (0.00)
0.09*** (0.00)
0.01*** (0.00)
Room map
-0.004** (0.00)
–
-0.01*** (0.00)
-0.07** (0.02)
–
Grid ratio
0.33*** (0.05)
–
0.39*** (0.07)
-0.32** (0.12)
–
Threshold2
0.21*** (0.00)
-0.48*** (0.02)
0.15*** (0.00)
-0.27*** (0.01)
-0.02*** (0.00)
Intercept
-0.22**
1.36**
-0.10
0.76***
0.06
Adjusted R2
0.83
0.55
0.85
0.28
0.26
BIC
-30,022.99
-6,114.63
-27,048.64
-18,914.03
-32,853.96
Standard errors are in parentheses
* p \ 0.05, ** p \ 0.01, *** p \ 0.001
Population: 40 agents
See Table 7.
Table 7
Symmetric network measure comparison (40 agents)
Independent
variable
Density
Average
distance
Clustering
coefficient
Eigenvector
centrality
Betweenness
Threshold
-0.32***
(0.00)
-0.40***
(0.02)
-0.40***
(0.00)
0.05*** (0.01)
-0.02***
(0.00)
Running
length
0.07*** (0.00)
0.64*** (0.01)
0.16*** (0.00)
0.08*** (0.00)
0.02*** (0.00)
Room map
0.05*** (0.01)
–
0.01*** (0.02)
–
–
Grid ratio
0.26*** (0.05)
–
0.36*** (0.08)
–
–
Threshold2
0.19*** (0.00)
-0.70***
(0.02)
0.10*** (0.00)
-0.18***
(0.01)
-0.03***
(0.00)
Intercept
-0.18**
1.53**
-0.11
0.41**
0.04
Adjusted R2
0.78
0.54
0.76
0.18
0.20
BIC
-29,849.2
-3,865.24
-24,276.8
-18,869.83
-34,137.72
Standard errors are in parentheses
* p \ 0.05, ** p \ 0.01, *** p \ 0.001
123
Factors of interest in agent-based socio-cognitive simulations
145
Population: 60 agents
See Table 8.
Table 8
Symmetric network measure comparison (60 agents)
Independent
variable
Density
Average
distance
Clustering
coefficient
Eigenvector
centrality
Betweenness
Threshold
-0.19***
(0.00)
-0.51***
(0.02)
-0.36***
(0.00)
0.03*** (0.01)
-0.02***
(0.00)
Running
length
0.04*** (0.00)
0.56*** (0.01)
0.11*** (0.00)
0.04*** (0.00)
0.02*** (0.00)
Room map
-0.02** (0.01)
–
–
0.05! (0.05)
–
Grid ratio
-0.09** (0.03)
–
–
0.23! (0.08)
–
Threshold2
0.12*** (0.00)
-0.82***
(0.02)
0.13*** (0.00)
-0.26***
(0.01)
-0.02***
(0.00)
Intercept
0.18***
1.74**
0.26**
0..10
0.08**
Adjusted R2
0.77
0.57
0.81
0.24
0.32
BIC
-36,536.88
-3,686.64
-28,199.56
-18,172.47
-42,935.08
Standard errors are in parentheses
* p \ 0.05, ** p \ 0.01, *** p \ 0.001
Directed ties
Population: 20 agents
See Table 9.
Table 9
Direct network measure comparison (20 agents)
Independent
variable
Density
Average
distance
Clustering
coefficient
Eigenvector
centrality
Betweenness
Threshold
-0.41***
(0.00)
-0.10***
(0.01)
-0.39***
(0.05)
0.08*** (0.00)
0.04*** (0.00)
Running
length
0.19*** (0.00)
0.28*** (0.01)
0.21*** (0.00)
0.02*** (0.00)
-0.01***
(0.00)
Room map
0.05** (0.02)
–
–
–
0.03* (0.01)
Grid ratio
0.19* (0.1)
–
–
–
0.12* (0.06)
Threshold2
-0.11***
(0.01)
-0.28***
(0.01)
-0.15***
(0.01)
-0.02**
(0.00)
-0.05***
(0.00)
Intercept
0.47***
0.96**
0.71***
0.07
0.09
Adjusted R2
0.79
0.29
0.76
0.07
0.05
BIC
-21,807.24
-9,449.68
-20,262.82
-22,790.75
-28,845.32
Standard errors are in parentheses
* p \ 0.05, ** p \ 0.01, *** p \ 0.001
123
146
C. Zhao et al.
Population: 40 agents
See Table 10.
Table 10
Symmetric network measure comparison (40 agents)
Independent
variable
Density
Average
distance
Clustering
coefficient
Eigenvector
centrality
Betweenness
Threshold
-0.37***
(0.00)
-0.23***
(0.01)
-0.39***
(0.00)
0.06*** (0.01)
–
Running
length
0.27*** (0.00)
0.20*** (0.01)
0.28*** (0.00)
-0.06***
(0.00)
-0.02***
(0.00)
Room map
–
–
–
–
0.02* (0.01)
Grid ratio
–
–
–
–
0.1* (0.05)
Threshold2
-0.04***
(0.01)
-0.29***
(0.02)
-0.06***
(0.01)
-0.08***
(0.01)
-0.03***
(0.00)
Intercept
0.39**
0.70*
0.47**
-0.05
-0.08
Adjusted R2
0.76
0.28
0.76
0.06
0.05
BIC
-21,326.68
-8,182.56
-20,146.43
-17,997.19
-30,998.11
Standard errors are in parentheses
* p \ 0.05, ** p \ 0.01, *** p \ 0.001
Population: 60 agents
See Table 11.
Table 11
Directed network measure comparison (60 agents)
Independent
variable
Density
Average
distance
Clustering
coefficient
Eigenvector
centrality
Betweenness
Threshold
-0.28***
(0.00)
-0.10***
(0.01)
-0.42***
(0.00)
0.14*** (0.01)
-0.01***
(0.00)
Running
length
0.18*** (0.00)
0.02* (0.01)
0.21*** (0.00)
-0.09***
(0.00)
–
Room map
-0.02! (0.01)
-0.13* (0.06)
0.04* (0.02)
–
-0.04***
(0.01)
Grid ratio
-0.15* (0.07)
-0.62* (0.28)
0.18* (0.09)
–
-0.20***
(0.03)
Threshold2
–
-0.66***
(0.02)
-0.04***
(0.00)
-0.15***
(0.01)
-0.02***
(0.00)
Intercept
0.51***
2.28***
0.39**
0.18
0.3***
Adjusted R2
0.79
0.37
0.81
0.15
0.11
BIC
-26,961.6
-8,110.41
-23,085.32
-17,580.27
-36,378.39
Standard errors are in parentheses
* p \ 0.05, ** p \ 0.01
123
Factors of interest in agent-based socio-cognitive simulations
147
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Changkun Zhao is a PhD candidate at the College of Information Sciences and Technology’s Applied
Cognitive Science Lab. He is interested in spatial memory modeling, information processing theory.
Ryan Kaulakis is a PhD candidate at the Applied Cognitive Science Laboratory in the College of IST.
His research interests are in model fitting in cognitive architectures, and soft-computing.
Jonathan H. Morgan is and a Ph.D student at Duke University and a former researcher at the College of
IST’s Applied Cognitive Science Lab with expertise in modeling social interactions and social
moderators, including the moderating effect that relative spatial positions have on group performance.
Jeremiah W. Hiam is a research assistant at the College of IST’s Applied Cognitive Science Lab. Game
design, AI in games, and psychology of gaming are his fields of interest.
Frank E. Ritter is on the faculty of the College of IST, an interdisciplinary academic unit at Penn State
to study how people process information using technology. He edits the Oxford Series on Cognitive
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Factors of interest in agent-based socio-cognitive simulations
149
Models and Architectures and is an editorial board member of Cognitive Systems Research, Human
Factors, and IEEE SMC Part A: Systems and Humans.
Joesph Sanford is a Ph.D student at the Department of Computer Science, Tufts University. Before that,
he was a research assistant at Applied Cognitive Science Lab of Penn State University.
Geoffrey P. Morgan is a PhD student in Carnegie Mellon’s Computation, Organization, and Society
program. Morgan has experience in developing autonomous robotic systems, self-learning systems,
cognitive models, and user-assistive systems. He is interested in organizational impacts on individual
decision-making and on optimizing organizational performance.
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