Predicting the trajectory of the evolving international cyber regime: Simulating the growth of a social network

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Social Networks 41 (2015) 72–84

Contents lists available at ScienceDirect

Social Networks

jo u r n al hom ep age: www.elsev ier .com/ locat e/socnet

redicting the trajectory of the evolving international cyber regime:imulating the growth of a social network

odd C. Lehmanna, James A. Rolfsenb, Terry D. Clarkb,∗

University of Michigan, United StatesCreighton University, United States

r t i c l e i n f o

eywords:yber securityegime theoryonstructivismgent-based models

a b s t r a c t

This paper presents an agent-based model of regime growth. States and the relations comprising a regimeare conceptualized as social networks. Regime growth is understood as the addition of ties between statesas they agree to work with one another. These ties are added as a result of the interaction between statebehavior and the structure of their relations. We apply the model to the emerging cyber security regime.
Based on reasonable assumptions of the nature of the current international system, the model predictsa bi-polar structure pitting two distinct blocs led by the two states with the greatest capacity to conductcyber conflict. However, if states either place increasing emphasis on the benefits of trade or if the morematerially powerful seek greater cooperation among themselves, linkages will develop across the twoblocs.
© 2015 Elsevier B.V. All rights reserved.

Although theories in international relations (IR) have long con-eptualized states and their relations comprising them in systemicerms, surprisingly little use has been made of social networknalysis (SNA). Part of the hindrance to wider use of SNA is thatetworks have been treated simply as one way to describe a par-icular mode of organization in international politics. For example,he international system has frequently been described as hierar-hical. As a consequence, the SNA toolkit has not been fully broughto bear in systematic analysis of the implications of the structureo both the states and inter-state relations that define that struc-ure. The wider application of SNA in IR has been further limited incope by the general dearth of network data on the internationalystem.

As better data collection and analysis tools have become avail-ble in recent years, SNA has begun to enjoy greater prominence.ore scholars are discovering SNA’s usefulness in describing and

nderstanding the structure of the international system. Hafner-urton et al. (2009) introduce SNA to the field by providing aomprehensive overview of how and why network analysis can
ontribute effectively to IR research. They explain concepts, princi-les, and methods of network analysis as they apply to internationalolitics, showing that the value of network analysis lies in “more
∗ Corresponding author. Tel.: +1 4022804712.E-mail addresses: [email protected] (T.C. Lehmann),

[email protected] (J.A. Rolfsen), [email protected] (T.D. Clark).

ttp://dx.doi.org/10.1016/j.socnet.2015.01.002378-8733/© 2015 Elsevier B.V. All rights reserved.

precise description of international networks, investigation ofnetwork effects on key international outcomes, tests of existingnetwork theory in the context of international relations, and thedevelopment of new sources of data.”

The most common approach to SNA in IR is to analyze staticproperties of a network to explore the structural relationshipsbetween actors at a specific point in time. While static approacheshave important value in describing structural properties, they can-not explain or predict change. Consequently, a dynamic networkanalysis approach holds significant promise in IR for understand-ing structural change in the international system. In this paper, weput forth a stochastic actor-oriented model (SAOM) to analyze thedynamic interaction between state behavior and system structure,which mutually condition one another. This allows for consider-ation not only of structural change but also behavioral change andhow the two might affect each other.

Given what appears to be a good fit between an emergentmethod and important analytical concepts in IR, it makes sense toexplore whether a SAOM for the dynamics of network and behaviormight contribute to better understanding certain processes withinthe international system. As Hafner-Burton et al. (2009) argue,“although many of the concepts embedded in network analysisappear to fit well with existing structural approaches to interna-
tional relations, that fit has yet to be empirically demonstrated.Network analysis will be most useful in international relationswhen it is carefully married to existing theoretical and conceptualapproaches and then helps to expand their scope.” To this end,
dx.doi.org/10.1016/j.socnet.2015.01.002

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dx.doi.org/10.1016/j.socnet.2015.01.002

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e propose that the SAOM for the dynamics of network andehavior can enhance IR scholars’ understanding of thegent–structure relationship in the international system.

In what follows, we lay the theoretical foundation in the IR lit-rature that informs our use of dynamic network analysis. We thenevelop the SAOM of the international system in which agent andtructure are mutually constitutive, where the agents are states thatxhibit distinct levels of cooperative or conflictive behavior, and thenstitutional relationships between states form a regime structures represented by ties in a complex network. In this model of thenternational system, the initial network-behavior configuration of

regime leads to the coevolution of states’ behavior levels andhe network structure over time according to the particular impor-ance assigned to states’ preferences and the subsequent strategicalculations made by states.

We then apply our model to a substantive issue that has emergeds one of growing importance in recent years: cyber security. Fol-owing the lead of Axelrod (1997), we construct an agent-based

odel to simulate the growth of the emerging cyber securityegime, conceptualized as an evolving social network comprisingtates (nodes) and the agreements into which they enter (non-irected edges). Homophily, or similarity in values or attitudes, canhus be captured by the ties between states; and the resulting struc-ure of these ties permits us to consider the effect of a regime acrosshe entire system of interactions. Regimes grow as the number ofies between states increases based on rules that govern the choicef ties. The choice rules constitute the environment within whichhe social network representing the system of states is embedded.

Results of the model’s simulations under reasonable conditionsf the current configuration of the international system predict aolarized Cold War-type structure pitting two distinct blocs led byhe two states with the greatest capacity to conduct cyber conflict.owever, if states either place increasing emphasis on the benefitsf trade or if the more materially powerful seek greater coop-ration among themselves, linkages will develop across the twolocs.

. Social network analysis in international relations

A social network analysis (SNA) approach views states as nodesnd relations between them as edges. This fits well with the conven-ion in IR of conceptualizing states and their relations as comprising

single international system. As Hafner-Burton et al. (2009) pointut, social networks not only permit scholars to consider the modef organization of the inter-state system, but network analysisermits them to consider the structural properties of that sys-em and their effect on states. Thus, it is not surprising to findhat increasing use has been made of SNA and network-orientedxplanations of international phenomena in recent years. Amonghe substantive issues considered have been alliance formationCranmer et al., 2012a,b; Warren, 2010), international trade andnvestment (Hafner-Burton et al., 2009; Jung and Lake, 2011; Kimnd Shin, 2002; Leblang, 2010; Manger et al., 2012), economicanctions (Cranmer et al., 2014), intergovernmental organizationetworks (Beckfield, 2008; Dorussen and Ward, 2008; Eilstrup-angiovanni and Jones, 2008; Hafner-Burton and Montgomery,006), terrorist networks (Eilstrup-Sangiovanni and Jones, 2008;verton, 2012; Kahler, 2009a, 2009b), human rights norms (Lakend Wong, 2009; Stein, 2009), policy diffusion (Cao, 2010), inter-ational conflicts (Faber, 1987; Kim and Barnett, 2007; Maoz, 2006,009, 2011), collective action problems (Scholz et al., 2008; Siegel,
009), world systems theory (Chase-Dunn and Jorgenson, 2003),nd democratic peace theory (Pevehouse and Russett, 2006).
Despite the burgeoning SNA research in IR, concerns have beenaised about potential shortcomings in applying network analysis.

works 41 (2015) 72–84 73

Two of the most common pitfalls are: (1) reducing networks tostatic properties of individual nodes (Hafner-Burton et al., 2009)and (2) failing to consider interdependence between the evolu-tion of the structure of the system and the behavior of states inthe system. A number of scholars have begun to address the firstpitfall through longitudinal studies and dynamic network analy-sis. For example, Everton’s (2012) work on developing strategiesto disrupt dark networks—i.e., covert and/or illegal networks suchas terrorist and criminal networks—is a crucial topic to considerfrom a dynamic perspective because, as he notes, such networksare quick to adapt and evolve due to constantly changing eventssurrounding the network. He discusses how longitudinal studies ofdark networks are highly promising and provides a brief overviewof some techniques to do so. Maoz (2006, 2009, 2011) also uses lon-gitudinal data to consider how international security interactionsand international conflict have changed between states over time.Other scholars, such as Cranmer et al. (2012a, 2012b, 2014), Mangeret al. (2012), and Warren (2010), have applied models specificallydesigned for dynamic and longitudinal network analysis to studyevolving international network structures.

However, very little has been done to explicitly address thesecond pitfall. Instead, when considering behavioral effects, scho-lars have typically attempted to parse out how state behaviorhas changed in response to network structure changes impres-sionistically. We attempt to avoid both pitfalls more rigorouslyby conceptualizing regime evolution and conditions for regimegrowth as a dynamically evolving social network in which bothstructure and behavior change in response to each other. Thenodes in the network are the states, and the ties between nodesare the institutional relationships between states in a regime.These ties are determined by the strategic calculation of states.Since the network is dynamic, we are able to consider the mutu-ally dependent relationship between the structure of network tiesand the attributes of the actors in the system. Conceptually, ourapproach presents significant potential for understanding aspectsof agent-structure processes in a complex and changing environ-ment. While the co-evolutionary network-behavior approach hasbeen applied to sociological issues—for example, to analyze thedynamics of friendship networks and delinquent behavior (Knechtet al., 2010), and to analyze the interdependent effects of academicperformance, friendship, and advice-seeking relations among grad-uate students (Lomi et al., 2011)—it has yet to be applied inIR.

Our approach conforms to the constructivist paradigm in IR.The three major paradigms in IR—neorealism, neoliberalism, andconstructivism—offer different approaches to understanding issuesof conflict and cooperation. The paradigms are not mutually exclu-sive, as there is some overlap in assumptions regarding states inthe international system. However, each provides a distinct lens tounderstand and explain international phenomena.

Under the assumption of a self-help anarchic system withexogenous interests, neorealists argue that structure is defined bymaterial power distributions that subsequently affect states’ abilityto pursue their interests in accordance with the structure. Conse-quently, states’ interactions are viewed as following the patternsof the material power structure in the system: structural changeoccurs according to changes in the material distribution of power(Waltz, 1979).

Neoliberals, on the other hand, grant neorealists the existenceof a self-help anarchic system, but instead suggest that regimesact as intervening variables (Krasner, 1981) that create complexinterdependence (Keohane and Nye, 2001), which confounds the
material power structure when actors have the proper incentivesto form institutions. Neoliberals therefore place stronger empha-sis on agency versus structure. For neoliberals, structural changeoccurs as states form institutions to address particular issues of

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ommon interest, with interaction and learning leading to peacefulnd cooperative conditions.

However, constructivism suggests a third possibility: the pres-nce of anarchy does not necessitate the assumption of a self-helpystem (Wendt, 1992) because interests are endogenous; struc-ure is comprised of both material and social forces, in whichatterned interactions are manifested as regimes that are bothause and effect of structure; and consequently structure and agentre mutually constitutive. Therefore, constructivism is opposed tooth a strictly materialist view (realism) and a view that interactionoes not have an effect on identities and interests (neoliberal-

sm) (Wendt, 1995). For constructivists, structural change arisesccording to path-dependent circumstances involving interactionsetween agents within the system that create endogenous effectsetween agents and the system’s structure.

A constructivist approach shares a number of overlappingoncerns with neorealism and neoliberalism. For example, bothonstructivism and neorealism focus on the role of structure in thenternational system. However, whereas neorealism predicts lesshange in the structure except when material power changes, con-tructivism argues that structural change is possible for reasonsther than material shifts (Hopf, 1998). Moreover, constructivistsrgue that neorealists do not take structure far enough, since theynly focus on how material structure affects state behavior, ratherhan how the more fundamental underlying social structure affectstate interests (Wendt, 1995). Yet just because structure is definedocially does not imply that change is easy or always possible.ather, the ease and level of structural change also depends onhe processes of institutionalization: “Even if interaction is initiallymportant in constructing identities and interests, once institu-ionalized its logic may make transformation extremely difficult.f the meaning of structure for state action changes so slowlyhat it becomes a de facto parameter within which processes takelace, then it may again be substantively appropriate to adopthe assumption that identities and interests are given (althoughgain, this may vary historically)” (Wendt, 1992). A constructivistccount of regimes, and their formal counterparts of institutions,s therefore driven by the view that institutions are a relativelytable structure of identities and interests “often codified in for-al rules and norms. . .[having] motivational force only in virtue of

ctors’ socialization to and participation in collective knowledge”Wendt, 1992). This view of institutions shares theoretical similar-ties with neoliberalism; the ultimate difference between the twoerives from that fact that neoliberals assume identities are exoge-ous and therefore cannot be changed, while constructivists arguehat identities are endogenous (Wendt, 1995).

A mélange approach to SNA in IR is offered by Maoz (2011),ho argues that the coherent structures and properties that arise

n international networks can best be explained by a theory ofetworked International Politics (NIP) that builds on the main

deas of neorealism, neoliberalism, and constructivism. NIP the-ry suggests that individual states’ decisions regarding whether toooperate with each other have direct impact on the network struc-ure that emerges from cooperative interactions. In practice, theheory’s assumptions derive primarily from neorealism and neolib-ralism regarding state behavior, with only a token constructivistpproach added. For example, the theory assumes that states areoncerned primarily with security under anarchy, that they seeko maximize their power as a way of ensuring their survival, andhat they are concerned with pursuing relative gains, all of whicherive from realist assumptions. Additionally, states’ inherent sus-icion of others is modified by issues such as common interests
nd previous beneficial interactions, which are primarily neoliberalssumptions. However, NIP theory incorporates constructivism byeducing the paradigm to a simple emphasis on culture and iden-ity and thus conflating it with culturalism, arguing only that states’
works 41 (2015) 72–84

identities and cultures affect behavior via their perceptions of eachother and the international system. While an emphasis on howidentity shapes behavior is one aspect of constructivism, NIP the-ory fails to directly incorporate the equally important endogeneityargument about states’ interests described above and thereforemisses an important opportunity to strengthen its explanatorypower.

This paper picks up where Maoz’s NIP theory leaves off by takinga constructivist approach in which agent and structure are mutu-ally constitutive, with changes in structure and agent behaviorbeing modeled as two dependent processes: the social selectionprocess and the social influence process, respectively, described indetail below. Within this perspective, the agents are states and theinstitutional relationships between states are represented as tiesthat make up the regime structure of the system. States determinewhether or not to join an institution based on strategic calculationswithin an existing structure initially determined by institutionaldesign. Moreover, states behave in a more cooperative or conflic-tive manner as both an outcome of the structure and as a force forstructural change. As other states enter into institutional arrange-ments, their relationships change the structure by creating newties, which then lead to changes in states’ preferences as to whetherthey will alter their institutional ties, or whether they will altertheir behavior. This process consequently creates a mutually con-ditioning loop that leads to further changes in the structure, states’strategic calculations, and states’ behavioral tendencies over time.

To this end, we develop a stochastic actor-based model of thedynamics of networks and state behavior. We then use the modelto consider the direction in which the emerging internationalcyber security regime will evolve as a consequence of the interac-tion between states as agents and their relations, the system. Theapproach taken here is not to precisely estimate empirical data, butto explore the critical limits of selected variables that can be usedto estimate plausible outcomes of international interactions.

2. The model

Our model is based on RSIENA, an R package that statisticallyestimates models for evolving social networks according to theStochastic Actor-Oriented Model (SAOM) (Ripley et al., 2014) andderived from Snijders (2005). Our model simulates the interdepen-dent evolution of network structure and states’ behavior in order toinvestigate how the design of a system of institutional ties affectsthe strategic relational ties across the entire network, and in turnhow the network-behavior configuration changes over time. Thefollowing characteristics and assumptions apply to SAOMs.

1. The network structure and individual states’ behavior levelsevolve through “micro-steps” that follow a continuous Markovprocess. At each step in the simulation, modeled as a single itera-tion, only one probabilistically chosen state has the opportunityto make one change, either to a tie or to its behavior level. Thischaracteristic reduces the overall change process into the small-est possible components in order to allow for relatively simplemodeling. When a change occurs to the network structure orto a state’s behavior level, it affects the entire system. Everystate in the system adjusts its preferred configuration in the net-work based upon the change. Each micro-step in the regime’sevolution process therefore impacts future structural and behav-ioral outcomes, the accumulation of which lead to the particularmacro-level structure that exists at the end of the simulation.

2. At a given point in time, the present network-behavior con-figuration determines probabilistically any further evolutionaryoutcomes. All relevant information is assumed to be includedin the current configuration, and any historical influences are

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incorporated into variables that contain relevant informationfrom the past (Snijders et al., 2010). This characteristic definespath dependence for the model.

. The underlying time parameter t is continuous.

. States have full knowledge of the current network-behavior con-figuration.

. States make their change decisions myopically, i.e., they decidewhether to change their ties or behavior according to the imme-diate result of the change without any knowledge of long-termnetwork structures that might result. Therefore, states in themodel are characterized as boundedly rational (van de Bunt andGroenewegen, 2007; Warren, 2010).

. States control their own ties on the basis of their network posi-tion, perceptions about the rest of the network structure andstates’ behavior, and individual and dyadic attributes. Likewise,states control their own behavior on the basis of the behaviorof the other states within their local network structure. There-fore, network ties and behavior are both controlled by individualstates but are mutually influenced by the network-behavior con-figuration.

. The model uses the basic principle that the first network-behavior configuration is not modeled but used as the startingpoint of analysis, so that X(0) and Z(0), the initial configura-tions of the network and behavior at time t = 0, respectively, aregiven. This principle implies that the primary focus of the anal-ysis is on the change over time after the initial configuration,and not on any inferences about what determines the network-behavior structure at the first point in time (Snijders et al., 2010).Therefore, any inferences about the initial configuration, e.g., ini-tial institutional design, must occur from theory external to themodel.

While the above assumptions and characteristics apply to ourodel, there are also significant differences between the RSIENAodel and the one we develop here. The most important dif-

erence is that RSIENA relies on longitudinal data sets defining network at several points over time. It then runs simulationsetween the empirical observations over time in order to determinebest fit” values for the model parameters that explain changesn the data. Our model specifies the parameters at the outset. Itequires only one network-behavior configuration that is used tonitialize the system at some start point. The network-behavioronfiguration then evolves from this initial configuration over 5000terations according to the particular weights assigned to states’references and the subsequent strategic calculations made bytates.

The model analyzes changes in network structure and changesn states’ behavior as two separate but dependent processes: theocial selection process and the social influence process, respec-ively (Snijders, 2011). The social selection process models states’references for ties with each other and therefore helps create theetwork structure. The social influence process models states’ pre-

erences to behave in a certain manner and therefore helps driveehavior throughout the system.

Let X(t) represent an n × n matrix at time t where xij is the rela-ion between actors i and j (i,j = 1,. . .,n). Thus xij = 1 indicates thexistence of a tie, and xij = 0 indicates the absence of a tie. The socialelection process is determined by a network objective function,hich is the weighted sum of the various structural and covariate

ffects of the relational matrix X(t). The function is formally defined
s,
[X]i

(ˇ, x, z) =(∑

k

ˇ[X]k

s[X]ik

(x, z)

)+ ε

works 41 (2015) 72–84 75

where the various effects are denoted by s[X]ik

(x, z) in which kdenotes a particular effect corresponding to state i’s attributesand tendencies given the present network-behavior configuration,ˇk corresponds to a weighted parameter for effect k, and ε is arandom element included to indicate un-modeled purposes andconstraints, and which prevents the network objective functionfrom being deterministic.

The nine network effects that are included in the network objec-tive function are listed in Eqs. (1)–(9) below. We chose these effectsaccording to a similar approach as Maoz’s (2011) NIP theory, whichargues that states seek security cooperation based on preferencesof relative material capability levels, levels of economic and institu-tional cooperation, levels of democracy versus autocracy, and levelsof cultural similarity. We also incorporated additional effects thatwe argue are important attributes for understanding how regimestructures emerge—including endogenous effects of the structureitself in (1) through (4) as well as a distance effect (5) and a behav-ioral similarity effect (9). It is important also to note that since themodel is comprised of a non-directed network, the principle of reci-procity between states is incorporated into the tie creation process,which is discussed further in “How the Model Works” below.

s[X]i1 =

∑j

xij Degree effect (1)

The most fundamental of the effects comprising the networkobjective function is the degree effect, which measures the overalltendency for a state to have ties. The value for (1) equals the num-ber of ties that a state has. It is expected that ˇ[X]

1 , the weightedparameter for the degree effect, will always be negative, indicatingthat ties are costly. Therefore, ˇ[X]

1 s[X]i1 will have a negative linear

effect on the objective function. Ceteris paribus, states will try tominimize the number of ties.

s[X]i2 =

√#{h|xih = 0, maxj(xijxjh > 0)} Indirect ties effect (2)

The indirect ties effect measures the structural effect for thenumber of others to whom state i is tied indirectly by geodesicdistance two, i.e., through one intermediary. This effect is an indi-cator of the benefit received for state i by having a connection tosome nearby state h via state j without paying the cost to estab-lish a direct tie with h. The square root of (2) is taken to illustratethat as the number of indirect ties for a state increases, then themarginal effect decreases, indicating that each subsequent indirecttie has less of an effect on a state’s objective function. Therefore,the functional form of (2) will have a diminishing curvilinear effecton the objective function, taking on either positive or negative val-ues. If ˇ[X]

2 is positive, then state i is able to positively benefit fromthe jh relationship and will find it more beneficial to maintain thestatus quo configuration than to establish a direct tie to state h;or, in the event that i has a tie with h, then i has an incentive tosever the tie. Therefore, when ˇ[X]

2 is positive, the effect measuresa tendency for states to prefer bilateralism, hierarchy, or broker-age, depending on the regime context in which it is used. Note thatthe intermediary state j generally has greater influence on the con-nected states due to the relative position within the configuration.Furthermore, a positive ˇ[X]

2 is expected when ties involve low riskof defection, whereas it should be negative if there is a high riskof defection (Berardo and Schulz, 2010). If ˇ[X]

2 is negative, state iwill view indirect ties as increasingly costly and will therefore pre-fer triadic closure by creating ties to indirectly connected states. In
this instance, states have a preference for multilateralism or gen-eralized exchange, and it is expected when ties involve high risk ofdefection. Ceteris paribus, and given a positive ˇ[X]
2 , states will tryto maximize the number of indirect ties. Ceteris paribus, and given

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negative ˇ[X]2 , states will try to minimize the number of indirect

ies via triadic closure.

[X]i3 =

∑j

xij

√∑hxjh Popularity effect (3)

The popularity effect indicates the tendency for states with highegrees to attract additional ties. More particularly, it is the ten-ency for state i to prefer having ties with more-connected othertates. Degree popularity is an indicator of centrality, status, andreferential attachment. The value for (3) equals the square rootf the number of ties that ego’s alters have, summed over alllters. This effect is expected to have a positive parameter for ˇ[X]

3ndicating that states with higher degrees are more attractive forthers to have ties with, which illustrates a bandwagoning effectn international regime growth. Therefore ˇ[X]

3 s[X]i3 will have a posi-

ive diminishing curvilinear effect on the objective function. Ceterisaribus, states will try to establish and maintain ties with moreopular other states.

[X]i4 = I{xi+ = 0} Isolate effect (4)

Previous research has noted that the extent to which a groupf actors becomes polarized is influenced by the patterns of socialelations (Buskens et al., 2008). Therefore, polarization betweenarticipating and non-participating states in the regime may existr arise as the network evolves. More specifically, it is expectedhat polarization will be most pronounced between states that aren the network and states that are outside the network. The isolateffect models polarization within the international system vis-à-is the regime, as it is a useful indicator for highlighting states thatre opposed to joining the network. Such reasons for oppositionould include domestic constraints, incompatible preferences, orundamental disagreements about the international regime. In thease of states that avoid isolation, the isolate effect can be consid-red a means of relativizing the cost of establishing the first tie withnother state. I {xi+ = 0} =1 if a state is an isolate, and 0 otherwise.herefore, if a state is isolated in the network, the effect will equal[X]4 * 1 and 0 otherwise. Since ˇ[X]

4 is an input variable that is speci-ed by the modeler at the outset, the relative influence that (4) hasn the network objective function will depend on the values for allther ˇ[X]

kinputs.

[X]i5 =

⎛⎝∑

j

xijDISTANCE3/2ij

⎞⎠

2/3

Distance effect (5)

Geographic distance is an important factor in the develop-ent of various regimes, including in preferential trade agreements

Manger et al., 2012) and in alliance formation (Warren, 2010).his expectation is due to the fact that many salient issues tendo arise in regionally clustered groups and therefore states in closeroximity will tend to form institutional linkages to address these

ssues. Geographic location for each state in the model is ran-omly assigned according to a two-dimensional x, y-coordinatealue on a 100 × 100 grid for each state. The distance between twotates DISTANCEij is calculated as the linear distance between the

wo points on the grid:√

(xu − xv)2 + (yu − yv)2. The value for (5)quals the sum of the geographic distances between ego and alllters. The distance value is transformed to indicate moderatelyncreasing costs for ties with more distant states. ˇ[X]

5 is expected
o be negative, which indicates that states prefer ties with geo-raphically close others. Therefore, ˇ[X]
5 s[X]i5 will have a negative and

lightly parabolic effect on the objective function. Ceteris paribus,tates will try to establish and maintain ties with states that are

works 41 (2015) 72–84

geographically closer.

s[X]i6 =

∑j

xij

(RPOLITY −

∣∣POLITYi − POLITYj

∣∣RPOLITY

)

× Domestic regime similarity effect (6)

Domestic regime similarity (Warren, 2010) uses the individualcovariate of a domestic regime score for each state to calculatea value that captures the tendency to prefer other states accord-ing to their domestic regime type, thus measuring one effect ofhomophily, or the tendency to prefer ties with similar others.POLITYi is the domestic regime score for state i, scaled between−10 and 10, where −10 is most autocratic and 10 is most demo-cratic. POLITYi for each state is derived from the Polity IV data set’s(Marshall et al., 2013) 2012 polity score, with any missing data filledwith a randomly assigned value. RPOLITY is the range of the domes-tic regime score for the entire network. The value for (6) equals thesum of the domestic regime similarity scores between ego and allalters. ˇ[X]

6 is expected to be positive, indicating that states preferties to others with similar domestic regime types. It is expectedthat states will cluster their ties around those with similar domes-tic regimes, so that ˇ[X]

6 s[X]i6 will have a positive sigmoid effect on

the objective function. Ceteris paribus, states will try to establishand maintain ties with states that share similar domestic regimetypes.

s[X]i7 =

∑j

xijTRADEij Trade effect (7)

Gains from trade between states are important to regime growthbecause they can create a spillover effect to other institutional rela-tionships. The higher the gains from trade that exist, the greaterthe expected likelihood that states will want to cooperate witheach other. The trade covariate is characterized in a dyadic fash-ion, such that the comparison between state i and state j is basedon a randomly assigned spatial variable in the model according to atwo-dimensional x, y-coordinate value on a 100 × 100 grid for eachstate. The farther a state is from another on this spatial grid (i.e., thegreater the distance), the higher the gains from trade exist betweenthese two states. The gains from trade between two states TRADEijare calculated as the linear distance between the two points on the

grid:√

(xu − xv)2 + (yu − yv)2 and then divided by 80 to scale thevariable in the computer model to a lower value. The value for (7)equals the sum of the trade levels between ego and all alters. Param-eter ˇ[X]

7 is expected to be positive, since states prefer ties withothers where gains from trade are higher. Ceteris paribus, stateswill try to maximize ties relative to higher gains from trade levels.

s[X]i8 =

∑j

xij|CAPABILITYi − CAPABILITYj| Capability effect (8)

The capability effect is the dyadic difference between states’material capability scores, which provides one measure for materialpower in the international system. Each state’s score in the modelwas derived from the National Material Capabilities data set’s(Singer et al., 1972) 2007 Composite Index of National Capability(CINC) score, with any missing data filled with a randomly assignedvalue. The CINC is a composite score for a state’s total population,urban population, iron and steel production, energy consumption,military personnel, and military expenditure of all state members.For our model, the CINC score was re-scaled between 0 and 100
and rounded to the nearest integer. The effect represents a mea-sure of the network impact of the dyadic distribution of materialcapabilities between states. The value for (8) equals the sum of thecapability difference between ego and all alters. Whether or not the

ial Networks 41 (2015) 72–84 77

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s

tobmftwiswwotoiibcnsiiita

rttntttcmia

Table 1Behavior levels.

Z(i) Behavior Level

0–10 Competitive


arameter ˇ[X]8 is positive or negative remains an open question at

his point. Warren (2010) finds a negative effect in his study onlliances, indicating that states prefer to ally with states possessingimilar capability levels. This is in contrast with Morrow’s (1991)xpectations that states prefer alliances with greater differences inapability levels because of the asymmetric benefits of influencend security received for the more capable and less capable state,espectively, which would be indicated by a positive value for ˇ[X]

8 .urthermore, different regime circumstances may yield differentesults. As Wendt (1995) notes, the meaning of the distribution ofaterial capabilities depends on the underlying structure: in some

nstances it is threatening for states when there is a greater dis-arity of capabilities, whereas in other instances it may make noifference. Consequently, different levels of both positive and neg-tive parameters for the capability effect can be simulated to betternderstand how this effect is related to the network structure.eteris paribus, and given a positive ˇ[X]

8 , states will try to maxi-ize ties relative to greater capability disparities. Ceteris paribus,

nd given a negative ˇ[X]8 , states will try to maximize ties relative

o lower capability differences.

[X]i9 =

∑j

xij

(Rz − |zi − zj|

Rz

)

× Behavioral similarity effect(Homophily) (9)

The final effect for the network objective function is theendency to prefer others who behave similarly. This tendencyverlaps with the separate behavior objective function describedelow and highlights the issue of network autocorrelation whenodeling the dynamics of network and behavior: positive values

or parameter ˇ[X]9 will contribute to positive correlations between

he behavior values of a state and the behavior values of others tohom the state is tied (Snijders et al., 2007). In other words, an

ncrease in ties to behaviorally similar others will actually lead thetate to change its behavior to become more like those states tohich it has ties; and conversely, a change in the state’s behaviorill lead the state to change its ties. This is simply another way

f saying that agent and structure are mutually constitutive. Theendency to prefer behaviorally similar others is a distinct aspectf homophily from the domestic regime similarity effect s[X]

i6 , buts calculated in the same manner. zi is the behavior score for state

according to Eq. (10) described below. The z variable is scaledetween 0 and 30, where 0 is most competitive and 30 is mostooperative. Rz is the range of the behavior variable for the entireetwork. The value for (9) equals the sum of the behavior similaritycores between ego and all alters. ˇ[X]

9 is expected to be positive,ndicating that states prefer ties to others with similar behavior. Its expected that states will cluster their ties around those with sim-lar behavior, so that ˇ[X]

9 s[X]i9 will have a positive sigmoid effect on

he objective function. Ceteris paribus, states will try to establishnd maintain ties with states that share similar behavior.

The social selection process models the changes in institutionalelationships between states over time, which result in changes tohe network structure. The nine effects above are summed togethero calculate the state’s network objective function. The value of theetwork objective function changes any time the network struc-ure changes or any time states’ behavior levels change. When givenhe opportunity to make a change, a state will calculate its objec-ive function for the current network-behavior configuration and
ompare the current value against the objective function values foraking a change over all other possibilities, probabilistically select-
ng the one action which maximizes its objective function: make positive change (add a tie), maintain the status quo (indicating

11–20 Individualistic21–30 Cooperative

satisfaction with the current configuration), or make a negativechange (sever a tie).

Additionally, let Z(t) represent the n × 1 vector at time t whereZi represents the behavior value for actor i (i = 1,. . .,n). The socialinfluence function is the means by which states change their behav-ior. It is determined by a behavior objective function, which is theweighted sum of various covariate effects of the states. The functionis formally defined as,

f [Z]i

(ˇ, x, z) =(∑

k

ˇ[Z]k

s[Z]ik

(x, z)

)+ ε

where s[Z]ik

(x, z) denotes the various effects, k denotes a particu-lar effect corresponding to state i’s attributes and tendencies giventhe present network-behavior configuration, ˇk corresponds to aweighted parameter for effect k, and ε represents a random ele-ment. The social influence function operates in the same manneras the social selection process above, in that a state will prob-abilistically select the one action that maximizes its objectivefunction, with the following options available: make a positivechange (increase the behavior variable by one unit), maintain thestatus quo (indicating satisfaction with the current behavior), ormake a negative change (decrease the behavior variable by oneunit).

The behavior objective function is linearly defined with zi char-acterized as an ordinal variable for state i calculated in the followingmanner:

zi = COOPERATIVEi

COOPERATIVEi + CONFLICTIVEiBehavior variable (10)

Therefore, a high proportion of cooperative interactions to over-all interactions would mean that a state has high cooperativetendencies for its behavior, whereas a low proportion would char-acterize more competitive states. The variable is scaled to valuesbetween 0 and 30 to allow for the range of behavior levels listed inTable 1.

The range of possible behaviors is defined here according tostates’ basic perceptions of the nature of the anarchic interna-tional system as characterized by Wendt (1999). The lowest ordinalvalue is assigned to those states viewing the international envi-ronment as competitive or “Hobbesian” in nature. The middleordinal value is assigned to those states viewing the internationalenvironment as incentivizing individualistic or “Lockean” behav-ior on their part. Finally, the highest ordinal value is reserved forthose states viewing the international environment as “Kantian” innature. Depending on these behavior levels, the predominant roleof states in the system will either be as enemy (Hobbesian sys-tem), rival (Lockean system), or friend (Kantian system). The socialinfluence process therefore models changes in states’ perceptionsof anarchy over time, which are expected to affect their behavior. Ata given point in time, each state considers a possible set of actionsto take in regard to its behavior: whether to maintain its currentassessment of the nature of the anarchic international system orchange it in favor of some other perception.

The four behavioral effects that are included in the calculation ofthe behavior objective function are listed in Eqs. (11)–(14) below:

s[Z]i1 = zi Linear behavior effect (11)

7 ial Net

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s

cttusiittnbbscmtsft

s

tmwo

−0e

ˇ

mrba

a

Titz

3

e

values for making a change over all other possibilities, probabilisti-cally selecting the one action that maximizes its objective function.For network changes, a state can make a positive change (adda tie),1 maintain the status quo (indicating satisfaction with the


[Z]i2 = zi

2 Quadratic behavior effect (12)

Taken together, (11) + (12) or ˇ[Z]1 s[Z]

i1 + ˇ[Z]2 s[Z]

i2 defines the globalendency effect and illustrates the unimodal distribution of theehavior variable in order to identify the behavior value that isreferred globally prior to taking the structure into account. Forxample, if the global tendency is modeled as a Kantian inter-ational system such that states prefer to be highly cooperative,egardless of their initial levels of cooperation, then the peak valueor the behavior value in (11) + (12) will be closer to 30. The peakalue of this global tendency can be calculated from the quadraticquation as zpeak = −ˇ[Z]

1 /2ˇ[Z]2 .

[Z]i3 =

∑j

xij

(Rz − |zi − zj|

Rz

)

× Behavioral similarity effect(Assimilation) (13)

Behavioral similarity characterizes the tendency for a state tohange its behavior based on the behavior of its alters in propor-ion to the number of alters. The basic behavioral tendency willherefore shift in value according to the state’s local network config-ration. The value for (13) equals the sum of the behavior similaritycores between ego and all alters. Note that mathematically, (13)s identical to (9) above. The difference between the two equationss that whereas in (9) the equation measures a tendency to preferies with similar others, in (13) the equation measures the impacthat the alters’ behavior has on ego’s behavior, proportional to theumber of alters. Consequently, (13) provides a means to analyzeehavioral assimilation. The issue of network autocorrelation onehavior is therefore dichotomized, measuring homophily in theocial selection process and assimilation in the social influence pro-ess. ˇ[Z]

3 is expected to be positive, indicating a tendency to behaveore similarly to others with which a state has ties. It is expected

hat states will cluster their ties around those with similar behavior,o that ˇ[Z]

3 s[Z]i3 will have a positive sigmoid effect on the objective

unction. Ceteris paribus, states will try to establish and maintainies with states that share similar behavior.

[Z]i4 = ziI{xi+ = 0} Isolate effect (14)

The last behavioral effect in the model measures the effecthat being isolated in the network has on behavior. This effect

odels the expectation that states that are isolated in the net-ork will behave differently than those that are connected to

thers. Specifically, the closer the global behavior tendency zpeak =ˇ[Z]

1 /2ˇ[Z]2 approaches to one pole (i.e., closer to a value of either

or 30), the more the isolate effect will have an opposing influ-nce on an isolated state’s behavior at the other pole. Consequently,[Z]4 = −2

(ˇ[Z]

1 + ˇ[Z]2 (zmin + zmax)

), where zmin and zmax are the

inimum and maximum behavior values for the entire network,espectively. To illustrate, consider a scenario in which the networkehavior values for z range between 0 and 30, as defined above,nd the basic behavioral tendency is to be cooperative (ˇ[Z]

1 = 0.5

nd ˇ[Z]2 = −0.01 so that the global tendency for zi is to equal 25).

hen the parameter ˇ[Z]4 = −0.4 results in an effect that drives the

solate behavior to zi = 5, the value for competitive behavior, sincehe local behavioral tendency of an isolated state is calculated as

isolate = −(ˇ[Z]1 + ˇ[Z]

4 )/2ˇ[Z]2 .

. How the model works

The simulation algorithm, which is described below, is used toxecute 5000 iterations so that the network and behavior evolve

works 41 (2015) 72–84

over a relatively large number of time “micro-steps.” Sensitiv-ity analysis is made possible by re-running the simulation underdifferent parameter values and determining how changes in theparameter levels affect the various network-behavior evolutionoutcomes.

The social selection and social influence processes are modeledaccording to the following five-step simulation algorithm.

1. Initialize the configuration of the system at t = 0 by defining X(0)and Z(0).

2. Randomly select a state i.3. Randomly select whether the next change will be a network or

behavior change according to the probabilistic weights for each.4. The change for state i is made probabilistically based on the

appropriate objective function’s present value.5. Go to step 2, unless the end of the period (i.e., number of itera-

tions) is reached.

A stochastic sub-process called the change opportunity processtakes place in steps two to three. This process is characterized bya rate parameter in RSIENA, which models the speed at which thenetwork and behavior level changes. For the purposes of the modeldescription here, it is only important to note that there are tworate parameters: one for the social selection process, and one forthe social influence process. The expectation is that these parame-ters can have different values, which indicates that change occursat different rates for each of the social processes. Therefore, sim-ulations can be run at different relative rates between the twoparameters to understand how more frequent changes to eitherthe network or behavior affect regime outcomes. These rates arecoded in our model according to probabilities of occurrence for thetwo processes, as determined by the modeler upon initializing thesimulation: for example, a 30% probability for the social selectionprocess and a 70% probability for the social influence process.

In step four of the algorithm, another stochastic sub-processcalled the change determination process takes place. The primarydriving force for any type of change in the model is the pair of objec-tive functions for network and behavior processes, which weredefined above in “The Model.” To better understand the concept ofthe objective function, consider the different interpretations thathave been used in previous studies. The objective function can beconsidered a measure of how “attractive” (Snijders, 2009) it is forstate i to change either the network or its behavior, summarized bythe state’s purposes and constraints. Snijders et al. (2010) frame theobjective function as the “rules for network behavior” of the focalactor. It could also be considered the preferred outcome or beststrategy according to the context in which it is used. In any case,state i attempts to “move into a direction of higher values. . .subjectto the constraints of the current network structure and the changesmade by the other actors in the network” (Snijders et al., 2010).

The value of the objective function changes any time the net-work structure changes or any time states’ behavior levels change.When given the opportunity to make a change, a state will calculateits objective function for the current network-behavior configura-tion and compare the current value against the objective function

1 Within the change determination process, SAOMs for non-directed networkscan follow a number of principles to address the issue of tie creation and deletion,such as a forcing principle, in which one actor takes the initiative and unilaterallyimposes a tie; requiring mutual agreement between pairs of nodes for a tie to exist;or requiring maximization of combined gains and losses between pairs of nodes such

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urrent network structure), or make a negative change (sever a tie).or behavioral changes, a state can make a positive change (increasehe behavior variable by one unit), maintain the status quo (indi-ating satisfaction with the current behavior), or make a negativehange (decrease the behavior variable by one unit).

Overall, states are assumed to be myopic in their determi-ation of their individual objective functions. This assumptionncompasses activities in which future outcomes are unknownnd unanticipated or unintended consequences can play an impor-ant role, so that each state can only know what is best for it at aiven moment based on the current network-behavior configura-ion and its preferred outcomes. Therefore, the objective functions,together with the current network-behavior configuration, implypecific global dynamics as emergent property of the individ-al changes, in which network actors are mutually constrainingach other and mutually offering opportunities to each other in aeedback process” (Steglich et al., 2010). Consequently, the modelncompasses the idea suggested by Sterling-Folker (2000) thathort-term behavioral cooperation can lead to the emergence ofore ingrained, long-term cooperation.

. Applying the model: predicting the evolution of themerging cyber security regime

Given the unique threat that cyber attacks pose to the inter-ational system, it is not surprising that scholars have begun toevote increasing attention to the issue of cyber security. Muchf this emerging literature has focused on strategies that statesight individually employ to deter cyber threats. In the tradition of

elf-help approaches, scholars have evoked Cold War deterrence ashe most viable strategy to promote security and prevent attacksAlperovitch, 2011; Geers, 2010a; Miller, 2011; Rice et al., 2011).thers have argued that cyber security issues should be treated as

law enforcement challenge (Schachtman and Singer, 2011). Thisould require that the international system work collectively to

dvance international law addressing cyber threats (Buchan, 2012;athaway et al., 2012; Nguyen, 2013; O’Connell, 2012; Tsagourias,012). The general argument has led some scholars to argue for the

mportance of an international cyber security regime. Such a regimeould give birth to norms and procedures that would reduce the

hreat to the entire community of states (Amin, 2010; Geers, 2010b;aurer, 2011).The realm of cyber interactions and vulnerabilities in the infor-

ation age is distinctly different from past historical structures that
ere built primarily on the basis of economic and material power.hile traditional power structures still drive much of the influ-
nce in the world today, the high interconnectedness and equal

hat gains for one may outweigh losses for the other (Ripley et al., 2014). Our modelocuses on strategic reciprocity by incorporating the principle of “unilateral initiativeith reciprocal confirmation” (Ripley et al., 2014) with the extension to allow a state

he ability to think one step in advance and consider the likelihood that anothertate will accept the proposed tie (Snijders, 2008). Our model therefore allows for

strategic representation of states’ calculations when considering tie proposals.o illustrate the full principle, the tie creation and deletion process by the focaltate i operates according to the following process: i takes the initiative and eitherroposes a new tie with j, makes no change, or dissolves an existing tie accordingo whatever action is most preferred. For new tie proposals, i will propose a tie to

based on i’s preference for a tie and the expected likelihood that j will accept theie (unilateral initiative with strategic consideration of expected likelihood); j mustonfirm the tie based on its own preferences (reciprocal confirmation), otherwisehe tie is not created (yes/no decision from j). However, confirmation from j is notequired in order for i to dissolve an existing tie. (While this strategic calculationdea was proposed by Snijders in a conference presentation at Oxford in 2008, were not aware of any reference to it elsewhere, including in the RSIENA manual.) Therinciple we use for tie proposals is plausible since most institutional relationshipsill not exist without mutual consent, and states are not likely to propose ties to

ther states unless they expect a high likelihood of confirmation.

works 41 (2015) 72–84 79

reliance by both state and non-state actors upon cyber networkscreates new security issues and the potential for new power struc-tures to be established. Furthermore, the cyber realm confoundsmany of the distinctions between public and private sector withregard to state security. Therefore, the emergence of a cyber secu-rity regime is expected to establish new structures of interactionbetween states that redefine sources of power in the issue area.Given that cyberspace constitutes a relational space, it seems ide-ally suited to social network analysis (SNA). Indeed, this point hasnot been lost on scholars. Hare (2009) employs SNA to argue thatthe most connected states in the international system are the mostvulnerable to cyber attack and therefore have the greatest inter-est in a cyber security regime. Hare and Goldstein (2010) employ asimilar approach to an analysis of vulnerabilities faced by defensefirms.

While scholarly interest has been moving toward treating cybersecurity in terms of a regime, scholars have yet to consider howsuch a regime might evolve. In what follows, we apply the modelto the emerging international cyber security regime to makemeaningful predictions about how the regime is likely to evolve.The emerging cyber security regime in the international systemis at the early stages of development, and there are numerousquestions about what a regime might looks like and how otherstates will be able to build agreements with each other on thebasis of such a complex system. While states’ public and pri-vate sectors will need to cooperative effectively in order for anycyber security regime to be successful, it is the policies betweenstates that will drive the regime’s development. Therefore, themodel presented here provides an opportunity to consider howan emphasis on different policy areas, either individually throughstate policies or collectively through a formal institution’s policies,might encourage a particular cyber security regime structure toemerge.

Several assumptions are made about the emerging cyber regime,which are incorporated into the model through the effect param-eter values and the initial configuration of the system. First, it isassumed that the emerging regime is a hermit-type world in thatno explicit regime structure currently exists (i.e., the simulation ini-tializes with an empty network). Additionally, it is assumed that theinitial behavioral distribution in the international system is Lock-ean (individualistic) with a Kantian (cooperative) global tendency,meaning that states’ behavioral values will be in the mid-rangeand, prior to structural constraints, states in the regime networkwill want to become more cooperative on cyber security issues.However, isolated states, i.e., states that exclude themselves orare excluded by others from cyber security regime relationships,will be polarized in their behavior and will be driven toward moreHobbesian (competitive) behavior.

We assume a system of 196 states representing the internationalsystem. Our simulation begins with no connections between states,and we assign an equal probability (50%) of choosing to considera change to either the network or behavior. We set the initial net-work parameters to the values in Table 2. The initial value for eachof these parameters was selected based upon sensitivity analysisconducted for each of the variables that determined the criticalvalue range that has the greatest impact on the network’s densityand structural outcome.

The degree effect is defined as reasonably negative to reflect theassumption that ties are costly and will require significant effortby states in terms of the level of cooperation needed to be estab-lished between public and private sectors for an effective cybersecurity regime to be built. The indirect effect and popularity effect
are best considered together. The former is −0.5 and the latter is0.5 to model the expectation that states will bandwagon (positivepopularity effect) once a regime begins to emerge, and states thatestablish an agreement will likely drive other states to establish

80 T.C. Lehmann et al. / Social Networks 41 (2015) 72–84

Table 2Emerging cyber security regime parameter values.

Effect Parameter Value Sensitivity range

Degree ˇx1 −0.035 −0.050 to −0.001Indirect ˇx2 −0.500 −4.000 to 0.500Popularity ˇx3 0.500 0.010 to 1.500Isolate ˇx4 −0.010 −0.200 to −0.0015Distance ˇx5 −0.002 −0.008 to −0.0001Domestic regime similarity ˇx6 2.000 0.010 to 4.000Trade ˇx7 1.000 0.010 to 10.000Capability ˇx8 0.0005 −0.100 to 0.002Behavioral similarity (homophily) ˇx9 0.500 0.010 to 4.000Linear behavioral effect ˇz1 0.500 –Quadratic behavioral effect ˇ −0.010 –

ats(tntterd

tivetmttsdscwsodidsWrt

dtiotstcbbltahd

z2

Behavioral similarity (assimilation) ˇz3

Isolate behavioral effect ˇz4

greements with them; at the same time, once states bandwagonhey will also want to expand their regime relationships with othertates in their friends’ connections so as to induce triadic closurenegative indirect effect) in order to develop a more tightly clus-ered structure and assure further cyber security within their localetwork neighborhoods. The isolate effect is close to zero to modelhe assumption that it will be less costly for states to be isolatedhan to join the regime, at least initially. Once the regime begins tomerge, states will have to consider the costs and benefits of tieselative to the slightly negative cost of being isolated in order toetermine whether it is still less costly to remain isolated.

The geographic distance effect is close to zero since it is assumedo have little influence on states’ preferences for ties, because cybernterconnectedness already crosses physical boundaries and coversast areas of space through the speed at which information trav-ls; therefore, the threat of cyber attacks for states is not limitedo those states closest to each other geographically in the same

anner that territory has been important in predicting conflict inhe past, and consequently it is assumed that geographic impor-ance is almost completely neutralized as an important influence ontates’ decisions for cyber security relationships. On the other hand,omestic regime similarity is expected to have a high influence ontates’ decisions. This is based on the assumption of real-world indi-ations that states are already beginning to develop relationshipsith each other on cyber security issues based on domestic regime

imilarities. For example, both the European Union and NATO, tworganizations that emphasize domestic regime similarity vis-à-visemocratically elected governments, are making a point of driv-

ng the discussion on cyber security issues and are attempting torive the emerging regime. However, states such as China and Rus-ia who are less similar in their domestic regime types than the

estern world are not expected to join or agree to a cyber securityegime being driven by the EU and NATO powers, and thereforehey may drive their own set of regime relationships.

Trade is expected to have a relatively high influence on states’ecisions as well, although there may be an improved outcome inhe cyber security regime if trade has greater emphasis placed ont by states. The impact that assured cyber security would haven the private sector’s ability to operate unencumbered by cyberhreats to information and infrastructure would vastly improvetates’ economic stability. However, states’ domestic regimes main-ain responsibility for cyber defense whereas the private sectorontrols the majority of the aspects that can resolve or exacer-ate cyber conflicts, and states continue to be constrained by theirureaucratic processes and lack of experience in streamlining col-

aboration with the private sector (Kempe, 2013). Consequently,
he trade effect is not as strong as it could be. Following this initialssumption, a contingency scenario will be modeled to considerow a higher emphasis on trade will affect the regime’s structureifferently.
1.000 0.100 to 7.000−0.400 –

The influence that material capabilities will have on the cybersecurity regime is expected to be weakly positive. The assumptionfor the positive value for the effect in Table 2 is that more materiallypowerful states have a preference to form ties with less powerfulstates because of the ease with which these types of relationshipscan be formed for security issues. However, the capability prefer-ence is only weakly positive because cyber attacks and defense arenot limited to only the most materially capable states, and there-fore material capability differences are not expected to be the mostdominant issue in establishing security relationships. Followingthe primary scenario’s assumption, a second contingency will beconsidered in which states have a preference for materially simi-lar states, and the regime outcome will be compared to the initialassumptions.

The last two variables for behavior are based on general assump-tions. The behavioral homophily effect is expected to be somewhatinfluential, as states are expected to want to form cyber securityrelationships to other states who have similar levels of coopera-tion. Finally, the behavioral assimilation effect is assumed to behigh, as states that form ties are expected to react and respond toeach other’s cyber security relationships in a way that drives theirbehavior toward similar levels.

All of the assumptions outlined above for the emerging cybersecurity regime correspond to the values in Table 2. These valuesare input to the model, which is then run for 5000 iterations persimulation for a total of 100 simulations. The result of this initialconfiguration is that the international cyber security regime tendsto emerge as bipolar in 74 of the simulations, with two distinctclusters that are not connected to each other. The remaining 26simulations result in two distinct clusters that share at least onenetwork tie across clusters. Thus, based on the expected outcomeof the simulations, the model predicts a distinct possibility of acyber Cold War. The two polarized clusters for one of the typicalsimulations in this first configuration are shown in Fig. 1.

Over 100 simulations, the cyber Cold War regime has a den-sity range between 12.30% and 13.19% with an average density of12.74%, which indicates a significant amount of growth within theregime from an initial density of zero. Additionally, after startingwith an average behavior value of 14.95, the emergent system’saverage behavior value has a range between 16.01 and 18.23 withan average of 17.16, indicating that a cyber security regime isexpected to slightly improve cooperation levels in the internationalsystem.

The results suggest that, if the assumptions for the emergingcyber security regime are correct, we will likely see two distinctregime types emerging on cyber security issues, and they will not
necessarily be compatible with each other. In fact, since the twoclusters in Fig. 1 have no connections between each other, it is rea-sonable to expect that the bipolar cyber security regimes will be atodds with each other.

T.C. Lehmann et al. / Social Net

eeddroii

psiis

imocstiltsittT

Fig. 1. Emerging cyber security regime structure.

Though it is the combined effects that will drive the regime tovolve into a bipolar structure, one of the critical factors is the pref-rence for domestically similar regimes. The left cluster in Fig. 1 isensely grouped together and is generally comprised of the moreemocratic states in the international system, meaning that democ-acies are expected to come to strong agreements with each othern cyber security issues and will band together. The right clusters less dense and comprised of states that are less democraticallynclined.

The model’s prediction may well be different if we consider tworeviously discussed possibilities. The first alternative to the initialimulation is that trade interests have greater emphasis than thenitial assumptions indicate. We model this contingency by increas-ng the trade effect in Table 2 to a value of 1.5. The effect on theimulation induced by this change is shown in Fig. 2.

Although there are still two clustered groups that emerge, theres an important difference in that a small subset of states act as

ediators between the two groups, linking them together. Outf 100 simulations, 90 result in a network with linkages betweenlusters, with the other 10 simulations resulting in a bipolar typetructure of two unconnected clusters, which therefore suggestshat an increased emphasis on the benefits from trade can lead tomproved cooperation. The network density and average behaviorevels are not dramatically different from the first scenario. Each ofhe clusters’ cores are dominated by the same states as in the firstcenario above, with stronger democracies tending to link together
n one cluster and stronger autocracies tending to link together inhe other cluster. However, the states that bind the two clustersogether play a pivotal role in maintaining the regime’s cohesion.hroughout the 100 simulations for the second scenario, the states
Fig. 2. Emerging cyber security re

works 41 (2015) 72–84 81

that most commonly emerge as “lynchpin” states are ones charac-terized as anocracies near the middle of the autocratic-democraticspectrum, and which tend to have little to no significant materialcapability. The lynchpin states are important because they straddlethe shared interests between both clusters, even if they are closer tothe periphery and may seem less powerful to the core states. Conse-quently, while a structure such as the one in Fig. 2 is fragile since itrelies on a few states to maintain the balance between the polarizedclusters, the outcome from this increased trade effect contingencymeans that there is the potential for collaborative cyber security inthe international system.

The second previously discussed alternative to the initial sce-nario is that states emphasize greater preference for similarityin material capability levels in determining their cyber securityregime relationships. In other words, the more materially power-ful states focus primarily on the relationship between each other,and the less materially powerful states prefer to assure each other’ssecurity in a regime.

We model this contingency by changing the capability weight inTable 2 to −0.1. The simulation outcome is illustrated in Fig. 3. Theimportant detail to recognize about the outcome is not so much thestructure of the regime, which is similar to Fig. 2; rather, it is thetwo isolated states that exist in the system. These isolated stateshappen to be the two most materially capable states in the model’sinternational system, and whose state characteristics are closelylinked to the United States and China from real-world data. There-fore, a strong preference for states whose material capabilities aresimilar will lead to a regime structure that does not include twoessential players for the success of the regime. Out of 100 simula-tions, 99 include both of these states as isolates from the rest of thenetwork, while the one remaining simulation had an isolated Chinaand included a single linkage between the United States and the restof the network. Again, the network density and average behaviorlevels are not dramatically different from the first scenario with theexception of the two isolated states, which have an average behav-ior level of 5.48 across the 100 simulations. This lower value reflectsthe polarizing effect of being an isolate, leading to more conflictivebehavior with regard to the regime than the rest of the network.

Furthermore, 50 simulations result in a network with linkagesbetween clusters, and 50 simulations result in a bipolar network ofunconnected clusters. Since the system’s structure relies on medi-ators between clusters when such linkages exist, and the mostpowerful players in the system do not back up these mediators,the long-term prospects for regime success in this second contin-gency are essentially non-existent. Generally speaking, althoughautocratic states and democratic states still cluster respectively,there is greater variation in which states play a primary role in the
core of each cluster. Notably, without China and the United Statesin the regime network, the more materially powerful states that doexist in the network do not ever emerge in the core for either clus-ter. Instead, there is a lack of coherence across the simulations with
gime—stronger trade effect.

82 T.C. Lehmann et al. / Social Networks 41 (2015) 72–84

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Fig. 3. Emerging cyber security regime

egard to which states can bind each of the clusters and the regimeogether, leading to an unpredictable and unstable outcome for theetwork that emerges.

On the other hand, the outcome from this contingency couldlso mean that a cyber security regime does not require the twoost materially powerful states in order to emerge. Therefore, if

he states comprising most of the international system do not wanto rely on these two power players for a regime to form, then theyould choose to construct a network of cyber security relationshipsy placing significant emphasis on the shared positions of materi-lly secondary and tertiary capabilities in the international system.owever, with only a 50% success rate of developing linkages acrosslusters for the third scenario, the risk of failure with this approachs much higher. Furthermore, since the two states with the sin-le greatest interest and influence in developing a cyber securityegime fail to join the rest of the network, the ability to regulate andnforce compliance and restraint would be severely diminished.ince the structure in Fig. 3 per se cannot determine which inter-retation is correct, policymakers must decide whether placingmphasis on similar material capabilities at the risk of excluding thewo most materially powerful states is a desirable outcome for thenternational system. However, the structural outcome provides alear illustration of the regime evolution and serves as a distinctarning that too much emphasis on similar material capabilitiesill isolate the most powerful states.

. Conclusions

The model’s prediction of a polarized Cold War cyber securityegime is within the realm of possibility and corresponds with whatome have speculated may already be developing. However, theontingencies considered here also highlight the important areasor policymakers to emphasize if they want to ensure a successfulnd collaborative cyber security regime: namely, the economic andrade benefits from improved collaboration between the public andrivate sectors, and the emphasis that states place on material capa-ility differences. The model’s outcomes from these contingenciesemonstrate that if decision makers can properly emphasize thesereas through their policies and negotiations with other states, ayber cold war is not inevitable.

The approach in this paper offers a means for analyzinggent–structure processes. It also has a number of interesting impli-ations. First, the approach in general, and the model in particular,llustrates how the accumulation of boundedly rational individualhanges can lead to the evolution of the system over time, includinghanges that lead to unintended consequences. Furthermore, such
hanges occur according to path dependence that can be tracedhange-by-change. Therefore, the historical context at institutionalreation and throughout the life of a regime matters. Additionally,hat may be a rationally designed institution in the beginning can
nger similar material capability effect.

evolve over time into something that is no longer “designed” in anyrational sense.

Second, while the model in this study is simulated over the longrun, Carley (1999) notes that, in reality, disruption typically occursbefore the long run outcome can be reached. Such disruption couldbe intentional in order to undermine the system. Everton (2012),for example, considers how dark networks might be disrupted forthe purposes of security and law enforcement. Such an approachto analyzing network structure could be inverted when consider-ing an emerging cyber security regime to study how to preventsuch disruption and destabilization, whether due to intentionalactions or by some type of exogenous shock. Furthermore, giventhat some level of disruption occurs, the question then becomeshow actors recover from disruptions, and how quickly this recov-ery occurs. Future research could attempt to better understandhow disruptions in regime development affect the paths towardgrowth, and whether and how quickly states can recover fromdisruptions.

Third, future applications of the model constructed in this studycould also include additional features that model other theoreticalissues and more complex factors. For example, a creation and/orendowment function could be added to the objective function inorder to account for calculations that may only be a factor whenconsidering either the creation or severing of ties, respectively.The creation function is used to model the gain in satisfactionincurred when a network tie is created, which could be tied to the-oretical arguments about spillover effects. On the other hand, theendowment function models the loss of satisfaction when ties aredissolved, which could be related to the concept of sunk costs or theprice of electing to invoke an escape clause (Rosendorff and Milner,2001) in an institution. As with the objective functions, the specificeffects included in either of these additional functions would needto be specified by the researcher in accordance with existing theory.

Finally, further research to expand network-behavior dynamicscould transform the exogenous variables in this model into endoge-nous variables that react to the structure of the system instead ofremaining fixed throughout the simulation. With this added com-plexity, research can conduct a more in-depth exploration of howstructure influences such variables as domestic regime types, tradelevels, and material capabilities, among any other possible variablesthat a researcher wants to study.

Ultimately, agent-based models of dynamic social networkshold significant promise for better understanding interactive pro-cesses of change in the international system. Such understandingshave previously been constrained by an assumption of indepen-dent units of observation contained within dyadic bubbles. Inparticular, agent-based models of dynamic social networks provide
a useful representation of the constructivist view of agents andstructures, in which international networks are social in nature.The effort to marry a tool for analyzing constructivist theory inthis paper offers a promising area for future research in better

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nderstanding the endogenous interactions of structures andgents in the international system.

cknowledgements

We wish to express our gratitude to the faculty and studentsf Creighton University’s Masters of Science in Data Science (DTS)rogram for their encouragement and support in the developmentf this project. We are particularly grateful to Sophie Wagner ofhe Creighton University Data Science program for her assistanceith the graphics. We are also indebted to Michael T. Heaney,ssistant Professor, Organizational Studies and Political Science,niversity of Michigan, and the faculty and students at the Univer-

ity of Michigan’s network working group for their helpful feedbackn an earlier version of this paper.

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