How Cooperation Emerges from Conflict: An Agent-Based Model of Security Networks Formation

Transcription

1 How Cooperation Emerges from Conflict: An Agent-Based Model of Security Networks Formation Zeev Maoz Department of Political Science University of California Davis Davis, CA and Distinguished Fellow Interdisciplinary Center, Herzliya, Israel April 2011

2 How Cooperation Emerges from Conflict: An Agent-Based Model of Network Formation Abstract This paper tests a theory of Networked International Politics (NIP) that explains how international security networks form and how they evolve. The theory asserts that states are driven to security cooperation by the wish to balance the capabilities of their Strategic Reference Group (SRG), those states that are perceived to pose a security challenge to the focal state. However, the process by which states choose allies depends both on common interest (shared enemies), common political affinities (joint democracy), and beneficial past interaction experience (shared trade and institutional ties). The predictions of the theory cover the process by which states seek allies, allies selection, and the emergent structure of security networks resulting from these choices. This process forms the basis for an Agent-Based Model (ABM) that explores the network implications of alliance formation and evolution. The ABM is tested on simulated data, as well as on real world data covering the period. We discuss the implications of the model and the empirical findings, in particular, the effect of strategic and affinity-related factors on the emergence of security cooperation networks, and the impact of network structure on systemic conflict.

3 1. Introduction Jean Jacques Rousseau viewed war as an endemic feature of an international system in which states depend on each other for their security (Hoffmann 1965: 62-63; Knutsen 1994: ). Yet conflict and war are not the modal form of international interactions. States cooperate with each other far more often and in considerably more diverse ways than they fight (Keohane and Nye 1987; Mansbach and Vasquez 1981). France, Germany, Japan, Russia, and the United States have lost millions of people in the two World Wars. Yet, both before and after the mutual slaughter, they had extensive trade and institutional ties with each other. Some of these enemies continued to trade while spilling each other s blood (Barbieri and Levy 1999). Moreover, both during and following rather intense conflicts, states forge cooperative links of various kinds. How can we explain the structure and evolution of different international networks? Can we account for the ways in which networks are formed, and the ways they change over time? This study extends the test of a theory of Networked International Politics (NIP) that explores processes of international network formation. The present study examines how global security cooperation structures emerge as a result of the calculations of policy makers about making and unmaking alliances. It integrates ideas drawn from the realist, liberal, and constructivist paradigms. I address several questions. 1. How do states decide to form cooperative security links with each other? 2. How do states decide with whom to form such links? 3. Is there a relationship between cooperation in non-security domains (e.g., economic, institutional) and security cooperation? 4. What kind of structural patterns emerge in the global system as a result of the cooperative choices of individual states?

4 The Formation of Security Cooperation Networks 2 The next section explores some issues in social network analysis and discusses the relevance of this approach to international relations research. 2. What Are International Networks? Why Should We Care? Social Networks Analysis (SNA) is a scientific framework for the analysis of emergent structures from complex patterns of relationships among units (organisms, people, nations). This perspective encompasses concepts, measures, and a methodological toolbox for the study of such structures. SNA seems a natural fit for the study of international relations. Yet, until recently this approach was used only sporadically. 1 Despite growing interest in this approach, many scholars are only vaguely aware of the key elements of SNA. Hence, I introduce some basic concepts. 2 A network is a set of nodes (states) and a rule that determines whether, how, and to what extent one node is linked to another. Networks analysts distinguish between relational and affiliational networks. A relational (or singlemode) network is one in which the rule defines a relationship between nodes. An alliance network is defined by the rule: state i has a formal alliance with state j. A trade network might be defined by the proportion of State i's GDP exported to state j. Affiliational (twomode) networks are those in which the rule defines the affiliation of a state with an event, institution, or group. International Governmental Organization (IGO) networks are defined by membership in IGOs (state i is a member of IGO k). Networks can be represented by graphs or by matrices. Figure 1 displays alliance networks at two points in time. Circles are states and arrows indicate alliances. Arrow width 1 See Hafner-Burton, Kahler, and Montgomery (2009) and Maoz (2010: Ch. 1) for a review of the growth in SNA applications to IR in recent years. 2 Maoz et al. (2005) and Maoz (2010: Ch. 2) contain a general introduction of SNA in IR. Wasserman and Faust 1997 and Jackson 2008 are comprehensive texts on SNA.

5 The Formation of Security Cooperation Networks 3 measures the level of commitment involved (see research design section). Circle sizes indicate the relative capabilities of the state, and colors denote regime types (red = democracy, blue = non-democracy). The density of alliances is considerably higher in 1974 than in In 1870 there is one dyadic alliance (between Brazil and Argentina), one four member block (Peru-Bolivia-Ecuador-Chile), and a more complex set of alliances in Europe with Germany/Prussia and the UK at the center of these structures. In 1974 we observe four clusters: marked by their well-known acronyms. However, multiple links exist across clusters, so that the more traditional division of the system into sets of collective security groups does not always fit the actual network structure. These pictures raise interesting issues regarding the structure of security cooperation and about changes of these networks over time. Figure 1 about here SNA allows derivation of network-related attributes of any individual node, the attributes of dyads, triads, groups such as cliques, blocks, or communities (Van Rossem, 1996; Kick and Davis, 2001; Hafner-Burton and Montgomery, 2006). We can derive emergent attributes of the entire system of relations. We can also measure a single characteristic of networks across multiple levels of analysis (Maoz 2009a). Networks can be partitioned into endogenously derived groups. I use here the concept of cliques. A clique is a closed subset of a network. Each clique is made up of units that are linked to each other at some minimal level. Cliques are not discrete; a node can be a member of any number of cliques. The only restriction is that a clique cannot be a proper subset of another clique, so that any two cliques must differ with respect to at least two members. Figure 2 about here Figure 2 shows the clique structure of the alliance networks from Figure 1. Squares represent cliques and arrows indicate clique membership. Some cliques are closed; their

6 The Formation of Security Cooperation Networks 4 members are not members of other cliques (e.g., cliques #5 and #6 in 1874). However, other cliques have some members in common. Several measures describe the structure of the entire network. The simplest is density the ratio of actual links to the number of possible links. Another important measure is transitivity or clustering coefficient (Watts and Strogatz 1998): the proportion of transitive triads in a network. A triad is transitive if it is closed: a link between node i and j and a link between j and a third node k entails a link between i and k. Components are closed subsets of reachable nodes. Cliques represent subsets of directly connected nodes. Components are groups of nodes that are reachable directly or indirectly. By definition, components are disjoint. Figure 3 shows the components derived from the two alliance networks. Figure 3 about here The Network polarization Index NPI (Maoz 2006b; 2010) measures the extent to which the network approaches a strictly bipolar structure. It is based on the clique structure of a network and on the overlap between cliques in terms of membership. With these concepts in mind, I turn to a theory of the formation and evolution of security cooperation networks. 3. A Theory of Networked International Politics (NIP) 3 The NIP theory is based on a number of assumptions about state behavior. 1. The principal concern of states in an anarchic environment is national security. 2. States seek to maximize their power as the principal way of insuring security. 3. International anarchy and states motivations (power maximization, pursuit of relative gains, and fear of cheating) render states inherently suspicious about other states. 3 This is a significantly condensed discussion. Maoz (2010: Ch. 5) provides a general discussion of the theory and its relation to the realist, liberal, and constructivist paradigm.

7 The Formation of Security Cooperation Networks 5 4. Nevertheless, the inherent suspicion of others is modified by: common interests, common identity, beneficial past interaction experience. These assumptions integrate ideas of the three leading paradigms of world politics. The first three assumptions draw upon the realist paradigm. The first two assumptions require no elaboration. The third assumption implies that states constantly seek to take advantage of each other. 4 Accordingly, cooperation is a necessary evil; states try to avoid it if possible. These assumptions pose a paradox: if states are out to exploit each other, then everyone is a potential enemy. Hence, states cannot insure their security without help from others. Yet, they are reluctant to cooperate for fear of being exploited. Assumption 4 seeks to resolve this contradiction: states impose filters on potential candidates for cooperation. The realist filter is the notion of common interests. In practical terms, states have common interests to the extent that they have common enemies (Mearsheimer 1994/5: 12-13; Maoz et al., 2007). The liberal paradigm asserts that democracies tend to trust each other more than they trust nondemocratic states, because they share norms of cooperation and peaceful conflict resolution (Maoz and Russett 1993). Just as states define future threats on the basis of past experiences a point I explore below they scan their environment for potential partners with whom they share mutually 4 Realists disagree about whether states opt for relative gains (Powell 1991; Snidal 1991a, 1991b). Defensive realists suggest that states seeking absolute gains opt for balance; offensive realists claim that states strive at dominance. I rely on the latter approach because it is more averse to international cooperation.

8 The Formation of Security Cooperation Networks 6 beneficial interaction. The constructivist aspect of these assumptions asserts that states tend to view each other as relatively trustworthy to the extent that they had shared positive economic or institutional interactions in the recent past (Jepperson et al. 1996). The following story emerges. States monitor their environment to identify security challenges. The states that pose direct and immediate national security challenge to a given state form its Strategic Reference Group (SRG). 5 Once leaders determine the composition of their SRG, they need to determine what kind of challenge these states pose to their nation s security. The military capabilities of the states making up one s SRG constitute the principal indicator of the nature and extent of this challenge. A worst-case scenario requires a given state to balance the aggregate capabilities of these potential adversaries. States whose capabilities outweigh the combined capabilities of their SRGs do not require allies; they can rely on their own resources to meet external challenges. In practice, most states cannot balance their SRGs by relying on their internal resources. Decision makers determine the magnitude of the security challenges they face by subtracting their nation s capabilities from the sum of the capabilities of the states constituting their SRG. This difference is the alliance opportunity cost what the state stands to lose if it fails to bolster its capabilities vis-a-vis the challenges emanating from its external environment. 5 The SRG concept is a refinement of the notion of Politically Relevant International Environments (Maoz 1996: ). The SRG of a given state consists of (a) all states with whom the focal state had a militarized interstate dispute over the past five years or an interstate war over the past decade, (b) all strategic rivals of the focal state, and (c) the allies of the states in (a) and (b) the allies of my enemies. An elaborate discussion and empirical validation of the definition of the SRG is provided in Maoz (2010: Ch. 4).

9 The Formation of Security Cooperation Networks 7 This reasoning helps determine (a) whether the state needs allies to thwart potential challenges, and (b) by how much it needs to augment its own capabilities in order to do so. The next question that decision makers contemplate is: who should be our allies? The answer to this question is covered by Assumption 4. Realists suggest that allies can be trusted to the extent that they share interests with the focal state. States share security interests to the extent that they have common enemies (Mearsheimer 1994/5: 13). Yet, the fewer allies, the better. An excessive number of allies is a prescription for trouble because they can drag the focal state into unwanted conflict, or they shrink the spoils of victory (Riker 1962). Thus, states look for the strongest possible partners to minimize the number of allies. The liberal paradigm asserts that democracies seek democratic allies because they view democracies as reliable and prudent. Non-democratic states adopt the enemy-of-my enemy principle. The constructivist paradigm asserts that interactions define ideational affinities and common identities. Consequently, decision makers are likely to trust those states with which they share a history of mutually beneficial cooperative links on such matters as trade or common IGO memberships. This suggests several propositions regarding national alliance behavior: P1. The higher the capabilities of the states making up the SRG of the focal state, (a) the more allies it is likely to seek, (b) the higher the capabilities of its allies. P2. The likelihood of any two states forming an alliance increases as (a) they share common enemies (c) the higher the capabilities of their respective SRGs, (d) the two states are democratic, (f) the two states share a history of positive economic and institutional cooperation.

10 The Formation of Security Cooperation Networks 8 These propositions form the first layer of the NIP theory. However, the central focus of a network approach is on the emergent consequences of these microfoundations. The focus is on the structure of the global security networks that emerge from these principles of individual and dyadic choices of alliance partners. Elsewhere (Maoz 2010) I discuss these structural implications at length. Here I focus on the fit between the process posited by the NIP theory and the actual structure of security cooperation networks. I develop an Agent-Based Model (ABM) that employs the rules of alliance seeking and ally selection deduced from the NIP theory. The data that activate this process (characteristics of the SRG, regime type, cooperative network links) are fed into the model and via the application of these rules are then converted into expected alliance networks. If the causal process stipulated by the theory is valid, the structure of these expected alliance networks should fit closely the structure of historically-observed alliance networks. The intuition here is straightforward: If all states follow these rules of alliance formation, the resulting networks that emerge should have identifiable characteristics. Given that the ABM captures the empirical reality of individual and dyadic choices, the resulting structures of security cooperation networks derived from this model should closely match the actual structure of security cooperation networks. Accordingly, we should expect that, P3. The process of alliance formation outlined by the NIP theory induces networks whose structures match those of real-world security cooperation networks, specifically, (i) (ii) (iii) the connectivity (density, proportion of components), polarization, group centralization of estimated networks due to the ABM are associated with parallel characteristics of historically-observed networks.

11 The Formation of Security Cooperation Networks 9 Finally, we started with the notion that security cooperation emerges due to the fear from, or the experience of, conflict. We close the circle by positing the effects of networking on conflict patterns. The NIP theory hypothesizes that security cooperation networks condition the behavior of members. Dense, polarized, and centralized networks are those in which many members are highly concerned with their own security. Such structural characteristics also imply that many states are committed to helping others who get in trouble. Under such conditions, the likelihood of systemic conflict rises. This is so because the system is both ideologically and strategically divided between a few groups composed of states with common security concerns, common affinities, and common enemies. Within such groups, conflict levels decline. Between-group conflicts are frequent and intense. Thus, P4. The expected characteristics of security networks affect the level of systemic conflict. Specifically, as the density, polarization, group centralization of expected security networks increase, the level of systemic conflict tends to increase as well. The next section outlines the features of the agent-based model of security networks. 3. Agent-Based Model (ABM) and Research Design 3.1. Why ABM? The propositions posited by the NIP theory have been tested via conventional empirical tests (Maoz 2010). The baseline models of alliance formation presented below also corroborate these arguments. Yet, such tests have a serious limitation: they do not provide direct evidence of the causal process of alliance formation and ally selection. The relationships between the independent variables and actual alliance structures may be due to processes other than the ones spelled out by the theory. The utility of agent-based models is threefold. First, ABMs allow analysis of networks that are more general than those that are permitted by available data. This opens the

12 The Formation of Security Cooperation Networks 10 door to analyses of emergent implications of the process posited by the NIP theory in ways that empirical analysis often cannot. For example, ABMs generate counterfactual scenarios given some fundamental changes in the conditions of the system (e.g., significant growth in its size, dramatic changes in the distribution of capabilities, significant spread of, or drop in conflicts). Second, ABMs allow tracing of complex dynamics, sequences of decisions, and emergent structures that cannot be easily tested in statistical models. The process posited by the theory is quite complex. This may induce statistical models with many variables, or with multiple interactions that are difficult to interpret. Moreover, temporal sequences in patterns of relations are apt to be lost in such models. In such cases, central ideas of the theory might be misrepresented by statistical models. Instead, the results of the ABM provide a parsimonious set of predictions that allow fairly simple tests of the theory s central tenets. Third, and most important, the ABM tests the causal dynamics of network formation. Hence, its results can be matched with the emergent structural properties of real world security networks. The fit between the model s output and the actual reality is not only a test of the final model s predictions but also of the process producing them. This allows a far more powerful strategy for assessing a theory than simply fitting the inputs asserted by the theory with the observed outcomes The General Structure of the ABM The following discussion covers the general intuition of the ABM. The appendix outlines in greater detail the process of alliance network formation produced by the model. Inputs: The ABM requires a number of input networks to operate. For each iteration (or each year when using real-world data), the following input networks are generated (or extracted from the historical data).

13 The Formation of Security Cooperation Networks Strategic Reference Network (SRN). This is an n n symmetric matrix with entry srn ij assuming a value of 1 if state j is in the SRG of state i, and zero otherwise. 2. Capability Vector (C). A vector of size n with entries c i denoting the share of the system s capability possessed by state i ( n c ii = 1). 3. Joint Democracy Matrix (D). Also an n n matrix with entries d ij assuming the value of 1 if states i and j are both democracies and zero otherwise. 4. MID Matrix. A symmetric n n matrix with entry mid ij =1 if states i and j had a MID and zero otherwise. 5. Joint Cooperation Matrix (JC). Again, a symmetric matrix with entries jc ij assigned 1 if states i and j had a history of economic and institutional cooperation, and zero otherwise. For the ABM runs with random data, entries in the input matrices are drawn at random with probability ranges reflecting the average values of these variables in the historical data. For the ABM runs with real-world data, the values in the matrices are assigned as discussed in the next section. The supplementary materials provide information about the distribution of the values in the various matrices as well as on the real-world data. First Iteration Step 1: A given state (i) identifies the members of its SRG. It then calculates the Alliance Opportunity Cost (AOC i ) by subtracting its own capabilities from the capabilities of its SRG. If AOC i 0 then the state does not require allies to balance its SRG, and the model moves to the next state. If AOC i >0, then the state begins the search for allies. Step 2: If the focal state is a democracy, it scans the system for democracies that are not in its SRG. Going from the strongest democratic partner to the weakest, the state adds sequentially the capabilities of a potential ally to its own capabilities and recalculates its AOC i. Once

14 The Formation of Security Cooperation Networks 12 the AOC i 0, the search for allies stops. If democracy i exhausts the set of non-srg democracies and still has a positive AOC, then it begins to behave like a non-democratic state. Step 3: A non-democratic state (j) starts its search for allies by looking for enemies of its enemies. The enemies of enemies are ordered from strongest to weakest. The focal state starts by adding the capabilities of the strongest enemy of enemy to its own capabilities and recalculating the AOC j. It continues to loop through enemies of enemies until one of two things happens: (a) AOC j 0, or (b) it exhausts the set of enemies of enemies and AOC j >0. Step 4: If condition (3.b) occurred, then the focal state goes to non-srg states with which it shared a history of cooperative relations. Here too, states are ordered from strongest to weakest, and the search continues until AOC j < 0 or these states were exhausted. Final Result of Iteration 1: The process produces an Expected Alliance Matrix (EA 1 ) with entries ea 1ij = 1 if state i considers state j as a potential ally and zero otherwise. This matrix is asymmetric (ea 1ij ea 1ji ). While state i may wish to form an alliance with state j, j may not necessarily be interested in an alliance with i. In such a case, no alliance is expected. Alliances are expected to form if and only if both states wish to do so. Thus the EA 1 matrix is symmetrized such that sea 1ij = sea 1ji = 1 iff ea 1ij = ea 1ji = 1, and zero otherwise. Subsequent Iterations: Each state now revises its SRG by incorporating the allies of its SRG members from the first iteration (based on the symmetrized EA 1 matrix) into its revised SRG. It then adjusts its AOC by adding its allies capabilities to its own capabilities and comparing this sum to that of the revised SRG. Once this was done, the state repeats the search for allies in the same manner as it did in the first iteration. Each subsequent iteration produces a new EA t and consequently a revised SRG matrix. The process is iterated until one of the termination rules is satisfied.

15 The Formation of Security Cooperation Networks 13 Termination Rules. Network formation ends when the one of two conditions is met: (1) the alliance network is at equilibrium. This happens when EA t = EA t-1, that is, SRGs are stabilized and alliance seeking stops. (2) The iteration process reaches a pre-specified maximum number of iterations (50). In such cases, the network did not converge into an equilibrium. The ABM produces a symmetrized expected alliance matrix for each iteration. These matrices are analyzed at different levels of analysis in ways described below. 4. Empirical Research Design Inputs of the ABM. To activate this model, I use two sets of input networks. One is a set of randomly generated matrices that stipulate the SRN, MID, Democracy, and Joint Cooperation networks. In addition a random capability vector C with entry 0 < c i <1, and c i = 1 provides the distribution of capabilities in the system. This allows us to trace the hypothetical evolution of alliance networks based on randomly generated input networks. The second set consists of historical data. This allows estimating the relationship between the predicted alliance networks produced by the ABM and the observed alliance networks. Spatial-Temporal Domain and Units of Analysis. The analyses focus on all states over the period of The basic network building block is a dyadic relationship. Data are arranged in a dyad-year form. The analyses encompass several units of analysis. The first unit is the stateyear. The second unit of analysis is the dyad-year. Since there is no a priori restriction on cooperative links between states, all dyads in the system are studied over their entire history. The third unit of analysis is the network (system) level. Each year is a network, and the evolution of real-world networks is traced over the entire period. Historical Data. Several datasets are used to derive network data. Some of these datasets are original and require some explication.

16 The Formation of Security Cooperation Networks 14 Contiguity. The contiguity dataset is derived from the COW project (COW, 2008; Gochman 1991; Stinnett et al., 2002), and covers all states over the period. Militarized Interstate Disputes (MID). The dyadic MID dataset (Maoz, 2005) covers all militarized interstate disputes over the period (Gochman and Maoz, 1984). Alliances. Leeds (2005) Alliance Treaty and Obligations Provisions (ATOP) project covers all formal alliances over the period. International Governmental Organizations (IGO). The IGO (Pevehouse et al. 2004) membership data are collected every half-decade for and annually for Trade. I rely primarily on the Oneal and Russett 2005 and Gleditsch 2002 datasets that cover dyadic trade between all dyads over the period. National Capabilities. The COW national capabilities dataset (COW, 2008, Singer 1990) covers all states over the period. Regime Structure. The POLITY IV dataset (Marshall and Jaggers 2004) covers all states over the period. Measures: (1) Dependent Variables. Alliances. For the nation-year unit of analysis I use several indicators of alliance. First, alliance degree centrality is the number of allies who have a defense or offense pact with the focal state, divided by n 1 (where n is the number of states for that year). Second, allies capabilities is the sum of capabilities possessed by the defense/offense allies of the focal state. Third, the level of alliance commitment is the sum of the level of alliance commitments across all the allies of the focal states, regardless of the type of alliance they have. The commitment score varies from zero to one and increases in the number of alliances and the level of commitment entailed in them. This index is explained at greater length by Maoz (2009a, 2010: Ch. 2).

17 The Formation of Security Cooperation Networks 15 At the dyadic level I use a binary variable defined as 1 if a dyad had a defense or offense pact at year t, and zero otherwise. The systemic measures include the following indicators of network structure: Alliance density: The number of dyadic alliance commitments for a given year divided by n(n 1)/2. Alliance transitivity: The number of transitive alliance triads (i j k i ) divided by the number of possible triads n(n-1)(n-2)/6. Alliance polarization (NPI). This measure is too complex to discuss here. It is explained in more details elsewhere (Maoz, 2006b, 2009b, 2010: 81-85). Briefly, it is a product of Clique Polarization (CPOL) an index of the polarization between membership in a given clique and all other states and Clique Overlap (COI) the extent of membership overlap between any pair of cliques. It varies between zero when all states are part of the same clique and one when the system strictly bipolar, that is, it is split into two equally powerful cliques that have no membership overlap. Alliance Group Centralization (Wasserman and Faust 1997: 180): GC n 1 i 1 (max AC ) AC ( n 1)( n 2) i [1] Where max ac is the alliance centrality score of the most central state, AC i is the centrality score of any other state, and n is the number of states in the network. Conflict variables. These variables are used in tests of P4, and measured at the systemic level. They include: (a) Proportion of MIDs: a ratio of the number of dyadic MIDs to the number of states at a given year. (b) Proportion of Wars: a ratio of umber of wars to the number of states. (c) Duration: sum of days across all MIDs at a given year.

18 The Formation of Security Cooperation Networks 16 (2) Independent and Control Variables. Some of the independent variables are used in baseline models of security networks. These baseline models are then contrasted with the predicted results from the ABM. 1. SRG Membership. The definition of the SRG is due to Maoz (2009a, 2010: Ch. 4). At the monadic level, this is the number of states in the SRG of the focal state. At the dyadic level, it is coded as 1 if dyad members are in each other s SRG, and zero otherwise. 2. SRG Capability. The sum of military capabilities (an average of the share of world military expenditures and military personnel) of all states that make up the SRG of a focal state. 3. SRG democratization. I use two measures of SRG democratization. One is the average Maoz-Russett (1993) regime score of states in one s SRG. The other is the proportion of states in one s SRG that are democracies (using the Maoz 1998: cutoffs for democracy). For the dyadic analyses I use the minimum regime score of the dyad. 4. Potential Democratic Allies. The number of democracies that are not members of the focal state s SRG. 5. Enemy of my enemy. Following Maoz et al. (2007), the enemy of my enemy (EE) matrix is defined as the binarized EE = MID 2. For the monadic analyses I define it as the number of the non-srg states that share enemies with the focal state. For the dyad-year unit of analysis I keep the original enemy of my enemy coding. 6. Ally of my enemy. This too follows the practice of Maoz et al. (2007). The Ally of my Enemy matrix is defined as the binarized matrix AE = MID A (where A is an alliance matrix with entries a ij =1 if states i and j had a defense/offense pact and zero otherwise. 7. Cooperation with non-srg. The average level of trade and institutional cooperation between a given state and all states that are not members of its SRG Maoz (2010: Ch. 6).

19 The Formation of Security Cooperation Networks Capability Concentration (CAPCON). The CAPCON index is based on Singer, Bremer, and Stuckey (1972) and Ray and Singer (1973). It the extent of the concentration of the system capabilities across states, varying from zero, when the distribution of capabilities is completely uniform to one, when one state controls all of the system s capabilities. 9. Proportion of Major Powers. Number of states designated as major powers (COW 2008) divided by system size. 10. Proportion of Democratic States in SRG Cliques. The density of democratic networks (Maoz 2010). This variable is expected have a negative effect on systemic conflict. Estimation: From Agent-Based Models to Empirical Testing A number of visual displays provide a general intuition of the agent-based model and the structural patterns that emerge from it. These demonstrate the emergence of cooperative structures in a pure sense, one deduced directly from the theory. Statistical estimates of the random-data ABM are provided in the supplementary material. The major test concerns the fit between the ABM output and the structure of historically-observed security cooperation networks. These tests focus on three levels of analysis. At each level I start with a baseline model of network formation that includes independent variables posited by the NIP theory to affect the formation of such networks. This allows a preliminary assessment of the theory. Subsequently, I estimate alliance variables using the ABM-derived estimates of such variables. At the national level, I estimate the actual number of allies for a given state and the capabilities of these allies using. At the dyadic level I estimate the actual presence or absence of a dyadic defense/offense pact. Finally, at the system level, I examine the relationship between the network characteristics of predicted security networks and the same characteristics of real world networks. 4. Results

20 The Formation of Security Cooperation Networks 18 I start with the results of the agent-based model with hypothetical data. Figure 4 presents three-dimensional graphs that show the effects of various characteristics of the attributes of the system on the structure of security cooperation networks. Figure 4 about here This figure and the statistical analyses in the supplementary materials suggest several points. First, the principal characteristics (density, polarization, and group centralization) of Strategic Reference Network (SRNs) have a strong impact on the respective structural indicators of alliance networks. This relationship holds across iterations. Second, the level of democracy in the system has a positive effect on the density of alliance networks in the initial iteration, but a negative effect on alliance density once the network converges. Joint cooperation has a similar impact on both the density and polarization of alliance networks. The general story, however, is simple. Security cooperation is highly sensitive to strategic factors the number and capabilities of SRG members and the overall characteristics of SRNs. However, as the network formation process evolves, agents revise their own position in terms of actual alliances they have formed and the characteristics of their security environment the changing structure of their SRGs. Once this happens, the initial structure of the security environment continues to affect networks, but the strength of this effect diminishes in proportion to other factors in this environment change. Joint democracy and past cooperation emerge as more significant factors that determine alliance choices as the process of alliance formation becomes more involved, that, is moves through more iterations. Second, the fit of the model improves at equilibrium. The fact that strategic factors (size and capabilities of SRGs) decline in importance relative to liberal (democratic density) or constructivist factors (joint cooperation density) tends to increase the fit of the model.

21 The Formation of Security Cooperation Networks 19 We now move to the analysis of the fit between actual alliance centrality scores of states over the period and the predicted degree centrality scores due to the ABM. Table 1 displays these results. Table 1 about here The baseline model regresses national alliance centrality scores on national and environmental attributes commonly used in the alliance literature (Maoz 2000, 2002, 2010: Ch. 7; Siverson and Emmons 1991; Gibler 2008a; Gibler 2008b). The results of the baseline model corroborate existing evidence about the determinants of alliances. First, the capabilities of the focal state s SRG form the motivation for alliances. Second, stronger states are more central members of alliance networks because they are more attractive alliance candidates. Third, the number of states that have common enemies with the focal state define the opportunities for alliance formation. Fourth, the interaction between the focal state s regime and the proportion of democracies outside its SRG consistently affects the alliance centrality of the focal state and the capabilities of its allies. The number and capabilities of a democratic state s allies increase as a function of the democratization of its potential allies pool. Finally, past cooperation between the focal state and non-srg members affects the focal state s allies capabilities, but not its alliance degree. Substituting the values produced by the ABM for the covariates in the baseline model suggests that the relationship between the predicted and observed values is highly significant. With respect to degree centrality, the first and final iteration of the ABM produce significantly lower mean root square errors than the baseline model. The intermediate iterations do significantly worse than the baseline model. With respect to allies capabilities, the ABM results provide a marginally better fit than the baseline model only in the final iteration. These results suggest that the process modeled by the ABM produces at least as good

22 The Formation of Security Cooperation Networks 20 and sometime better predictions of alliance degree and the capabilities of allies than a more complex input-output model. Table 2 about here Table 2 shows the tests of dyadic alliance formation. The baseline model replicates previous studies of dyadic alliance formation. With the exception of dyadic trade, the independent variables significantly affect the probability of alliance formation. The large number of observations implies that even a marginally nonzero coefficient is likely to be significant. However, the goodness of fit statistics indicate a general support for the baseline model. The improvement in fit model over a naïve prediction based on modal categories is also quite high. The results are robust with respect to alliance types. Substituting the variables in the baseline model with the ABM-predicted alliances suggests four key results. First, the association between the predicted alliance score of a dyad and the actual dyadic score is quite high. Second, these effects are robust across iterations and across alliance types. Third, the overall fit of the ABM model drops compared to the baseline model; so do the marginal improvement in fit scores. However, the drop is not very high given that the ABM-predictions are more parsimonious than the baseline model. Fourth, the fit between the ABM-related prediction and actual behavior is better for the first iteration than for the last one. It is not clear why that is the case, but one speculation may be that many political leaders apparently engage in relatively simple, one-shot selection process; only few engage in a more complex iterative one such as the one envisioned by the ABM. The most interesting and central aspect of the investigation of alliance network formation concerns the emergent structure of alliance networks. Table 3 displays the results of the estimated structural characteristics of alliance networks. Table 3 about here

23 The Formation of Security Cooperation Networks 21 I discuss each of these characteristics separately. 6 First, as a general rule the connectivity of a network is inversely related to the proportion of components. This serves as the foundation for interpreting the results of the baseline model in the leftmost column of Table 3. The results suggest that democratization and conflict reduce alliance network connectivity. On the other hand, as the proportion of major powers increases, so does alliance connectivity. Major Powers attract many allies, thus leading to a greater overall connectivity. The fit between the estimated proportion of components in the ABM and the actual proportion of components is not high. The ABM estimates perform less slightly better than those of the baseline model. On the other hand, the fit between the ABM estimates and actual network polarization is quite good. The baseline model suggests that systemic democratization reduces network polarization while the proportion of major powers increases polarization. Substituting these variables by the ABM estimate results in a marked improvement in fit. The group centralization index yields a similar result. The baseline model shows that centralization increases with the democratization of the international system and with the proportion of major powers. The ABM estimates fit the actual level of alliance network centralization quite well, and the overall fit of the model with ABM estimates is almost triple that of the baseline model. I highlight the general evolution of alliance networks induced by the ABM and their fit to the structure of real world alliance networks in Figure 5. Figure 5 about here 6 Analyses of additional network characteristics (density, transitivity, and group centralization) are given in the supplementary material and the replication website.

24 The Formation of Security Cooperation Networks 22 The final leg of the empirical analyses focuses on the effect of network structures on international conflict. Table 4 displays the tests of P4. Table 4 about here The baseline models suggest several things. First, the density of actual alliance networks has a negative impact on the proportion MIDs. On the other hand, the polarization of real world alliance networks has a positive effect on the proportion of wars and the duration of MIDs (Maoz 2006). Second, the proportion of major powers in the system has a positive effect on systemic conflict. Third, the proportion of democratic cliques tends to have a negative impact on the level of systemic conflict. Substituting the predicted NPI produced by the ABM for the independent variables in the baseline model yields consistent effects of network polarization on conflict. As the expected alliance polarization level increases, so does the level of conflict. The fit between the models using the expected alliance NPI and the actual conflict data is significantly better than the baseline models and the conflict indices. This suggests that the ABM s estimates of polarization provide a more accurate prediction of systemic conflict than the characteristics of real-world alliance networks. This may imply a latent process connecting the national and dyadic calculus of alliance formation to systemic structures. This is an important result. Since NPI increases as the system approaches bipolarity, this result casts serious doubt on the main prediction of structural realism (Waltz 1979; Mearsheimer 1990, 2001): increasingly bipolar systems tend to be more conflict prone than ones that are more multipolar in nature. Overall, the ABM seems to capture a fair amount of variance in individual, dyadic, and systemic patterns of alliance formation and maintenance. The logic of the NIP theory seems to generate interesting insights into the formation and evolution of security cooperation networks. These insights combine ideas from the three major paradigms of IR and

25 The Formation of Security Cooperation Networks 23 jointly offer a novel and integrative conception on the formation of a key set of networks that shaped international politics over time. The key weakness of the theory, as exemplified by the gaps between the ABM output and the observed structure of alliance networks, is that it seems to capture only a portion of a more complex web of calculations leading to the formation of such networks. Specifically, the model seems to underestimate the connectivity and transitivity of security cooperation networks. I discuss some of the possible reasons and implications of this deficiency in the concluding section. 5. Conclusion Two of the more prominent models of network formation rely on the concepts of preferential attachment and homophily. The preferential attachment model asserts that the probability of a new node forming a link with an existing node is a function of the centrality of the latter. The structural implication of the preferential attachment model is the wellknown power-law degree distribution (Barabasi and Albert 1999, Caldarelli 2007). 7 There is some evidence that the structure of security networks is not random. However this is only the case if we drop all isolates and dyadic alliances (with 0 and 1 degrees, respectively). That eliminates nearly 45 percent of the nation-years. The homophily model asserts that new nodes attach to existing nodes with similar attributes (McPherson et al., 2001; Currrarini et al. 2009). This results in another general structural feature: closed communities, with nodes within communities having similar attributes and nodes across communities having different attributes. The evidence provided 7 The power law asserts that the fraction of the nodes with k links (k degree) is defined by P(k) k where 2 3.

26 The Formation of Security Cooperation Networks 24 in the baseline models introduced in Tables 1-3 suggests a fair amount of homophily in security cooperation networks. A related study suggests that there is no significant evidence for preferential attachment in security network formation processes. Rather, the homophily process entailed in the ABM seems to provide a fairly good fit to the structure of real-world alliance networks (Maoz 2011). The key insights of the NIP theory seem to be supported by the empirical tests: security cooperation is induced by the reality or anticipation of conflict. This is what drives states to form alliances in the first place. But security considerations are not the only motivation, nor are they the principal determinant of which alliance form and what kind of global security structure emerges. Various types of affinity, due to liberal factors (joint democracy) and constructivist identity-related factors (cultural similarity, beneficial past cooperation) have a meaningful impact on the structure of security cooperation networks. This suggests that an integrative approach to security cooperation as outlined in the NIP theory seems to be a better approximation to real world network formation process than any of its parts. The sequence by which these considerations emerge in the calculus of alliance is also important. It varies for different types of states with democracies emphasizing common political affinity, and autocracies emphasizing common interests. Finally, as the NIP theory argues and as the results of the present study confirm, the structure of security cooperation networks has a significant effect on systemic processes of peace and war. Highly connected, polarized, and centralized networks are associated with high levels of systemic conflict. This applies surprisingly more to the characteristics of ABM-produced networks than to actual ones. This may suggest a vicious circle of conflictsecurity cooperation conflict. Without modifying effects of other types of cooperative networks, this process seems to propel itself.

27 The Formation of Security Cooperation Networks 25 Yet, the ABM seems to possess two key deficiencies in its ability to explain realworld alliance formation processes. First, the ABM underestimates the number of alliances by a wide margin. The actual average alliance degree is 9.79; the ABM average degree is , 6.12 for the first, intermediate, and final iteration, respectively. Likewise, the actual frequency of alliance-years is 0.103, while the frequency of ABM-predicted alliance years is 0.057, 0.065, and for the first, intermediate, and last iteration, respectively. Differences of proportions are highly significant. Second, there is a significant degree of inconsistency in real-world alliances. The average transitivity of real-world alliance networks is This implies that about 36 percent of all triads in the network are open triads. The homophily idea that is built into the ABM produces a significantly higher degree of transitivity in the predicted networks. Average transitivity scores are 0.83, 0.85, and 0.86 in the first, intermediate, and last iteration of the ABM, respectively. Historically, states were more likely to form alliances with members of their SRG that is, with actual or potential rivals than would be expected by chance alone. Over 31 percent of all dyadic alliance years involved such cases. These patterns are wellknown (e.g., Bueno de Mesquita, 1981; Maoz et al., 2007). The problem is to incorporate these inconsistencies into a stylized model of network formation. We may be able to improve the performance of the ABM once we have a better understanding of the causes of such inconsistencies in alliance formation. On a more general level, this study sheds light on important aspects of the evolution of international relations. The theory of networked international politics asserts that states behavior is governed by two contrasting realities. One is the anarchic nature of the international system that engenders constant concerns about security and survival. The inability to insure survival via mobilization of domestic resources drives states to security cooperation.

28 The Formation of Security Cooperation Networks 26 The other is that of inherent interdependence. Interdependence goes beyond the need to balance against common enemies. It creates affinities that spill over into the security realm. These realities shape the calculations of political leaders, and consequently the ties that states forge. Such micro dynamics culminate in generalizable structures at the system level. The simulated and empirical data support the ideas that the experience or expectation of conflict gives rise to security cooperation. But the evidence also suggests that security cooperation is driven by political, economic, and cultural affinities. This is much less well known or empirically established. Concomitantly, non-security networks have a spillover effect into security cooperation. These patterns have important implications for the structure of security cooperation. Here are some examples. Democracies have twice as many allies, on average, than autocracies and 1.5 times than anocracies. The capacities of the allies of democracies average twice those of anocracies and of autocracies. All these differences are statically significant. Finally, imbalanced allies states that are in each other s SRG but have an alliance are nearly twice as likely to be democracies, and to have a history of trade ties and IGO membership than SRG members without alliance. It therefore seems that common identity that is formed both by political affinities and by a history of cooperative relations seems to account also for the significant level of imbalance in alliance structures. The combination of agent-based modeling and network analysis offers a promising approach to the modeling of international processes. Much needs to be done, and many aspects of the theory, models, and methods can be improved. The current results suggest, however, that this effort is worthwhile; it generates interesting and novel insights into the processes of network formation and their structural implications.

29 Table 1: Determinants of Alliance Networks Actual Determinants and ABM Results: Nation-Year Unit of Analysis Time-Series Cross Sectional Analysis, all States, Alliance Degree a Allies' Capabilities b Baseline ABM Estimates Baseline ABM Estimates Model First Iteration Intermediate Last Iteration Model First Iteration Intermediate Last Iteration ABM Expected Allies 0.018** 0.012** 0.014** 0.327** 0.324** 0.018** (2.41e-04) (2.71e-04) (2.101e-04) (0.01) (0.005) (2.41e-04) SRG Capabilities 0.117** 0.196** (0.014) (0.005) Status 4.30e-04** 7.03e-04** 2.17e-04** 7.58e-04** 4.53e-05** 9.20e-05** 6.36e-05** 7.03e-04** (1.00e-04) (8.73e-05) (6.01e-06) (8.47e-06) (4.15e-06) (3.98e-06) (1.31e-06) (8.73e-06) Focal State Capabilities 0.067** 0.004** (0.002) (0.001) Regime Non. SRG Democs. 4.11e-04** 4.98e-05** (4.22e-06) (2.06e-06) Non. SRG Enemies of Enemies 1.281** 0.095** (0.041) (0.016) Past Cooperation with ** 0.022* Non-SRG states (0.028) (0.009) Cultural Similarity w. Non-SRG -6.84** ** states (0.069) (0.025) Constant ** ** 2.463** 0.098** 0.078** 0.072** 0.048** (0.032) (0.016) (0.006) (0.004) (0.002) (0.001) (0.001) N 12,445 12,228 53,879 12,665 12,779 12,565 53,879 13,016 No. of States Wald Chi-Square (F-Statistic ) 45, , , , , , , Difference between Baseline and ABM RMSEs d 3.76** ** 5.73** Adjusted R-Squared a Fixed-effects Time-Series Cross Sectional (TSCS) negative binomial model. b Fixed-effects TSCS regression c OLS model (Clustered on state). Fixed effects TSCS models cannot be run here because of repeated time values within panels. d Two-Sample T-Statistic

30 Table 2: Dyadic Alliances Baseline Model and ABM Results: All Dyads, Logistic Regression Baseline Models ABM--First Iteration ABM--Interim Iteration ABM--Last Iteration All Alliance Def./Off. All Alliance Def./Off. All Alliance Def./Off. All Alliance Def./Off. Types Pacts Types Pacts Types Pacts Types Pacts ABM Predicted Alliance 0.509** 0.786** 0.389** 0.425** 0.441** 0.536** (0.0184) (0.0233) (0.0103) (0.0153) (0.0218) (0.0228) Regime Score 0.007** 0.004** (0.0003) (0.0003) Trade (0.633) (1.0286) Joint IGO Membership 2.291** 2.006** (0.0456) (0.0551) Distance 3.72e-04** 3.149e-04** 4.72e-04** ** ** ** ** ** (5.50e-06) (6.41e-06) (3.09e-06) (4.85e-06) (2.50e-06) (3.19e-06) (4.31e-06) (4.82e-06) Minimum SRG Capabilities 0.165** 0.405** (0.038) (0.0431) Common Enemies 0.584** 1.096** (0.0784) (0.0885) Cultural Similarity 2.539** 3.237** (0.0586) (0.0672) Status 0.043** 0.044** 0.050** 0.059** 0.07** 0.087** 0.06** 0.059** (0.002) (0.0021) (0.0014) (0.0016) (0.0009) (0.0013) (0.0014) (0.0016) Non-Alliance Years ** ** ** ** ** ** ** ** (0.046) (0.0645) (0.0269) (0.0286) (0.0314) (0.055) (0.0269) (0.0355) Constant 1.298** 0.627** 1.564** 0.886** 2.425** 2.893** 2.278** 1.356** (0.0421) (0.0769) (0.0298) (0.0086) (0.019) (0.0115) (0.0152) (0.0193) N 623, , , ,691 3,425,712 3,425, , ,692 Chi-Square 47, , , , , , , , R-Squared MIF Marginal Improvement in Fit = (PCP P MC )/(1-P MC ) where PCP is the percentage of cases predicted correctly by the model, and P MC is the proportion of cases in the modal category.

31 The Formation of Security Cooperation Networks 29 Table 3: Relationship between Systemic ABM Prediction and Actual Alliance Networks Characteristics, Time-Series Regression, Network Characteristic Proportion of Components Network Polarization Group Centralization Baseline ABM Estimates Baseline ABM Estimates Baseline ABM Estimates Model First Last Model First Last Model First Last ABM Network 0.043* 0.055** 0.225** 0.251** 0.394** 0.318** Characteristic (0.021) (0.017) (0.058) (0.044) (0.105) (0.095) Democratic Cliques 0.225* * 1.09** (0.11) (0.017) (0.368) Prop. MID Dyads 0.042* * (0.017) (0.003) (0.197) Capability Concentration (0.344) (0.052) (1.178) Prop. Major Powers * * * 0.466** 0.336** 0.311** ** 5.73** 6.829** (0.517) (0.497) (0.489) (0.073) (0.068) (0.073) (1.244) (1.5) (1.504) Constant ** 0.048** 0.049** * * (1.879) (0.687) (1.299) (0.023) (0.012) (0.012) (0.438) (0.137) (0.144) Rho Model Statistics N F Adj. R-Squared D-W Statistic Notes: * p < 0.05; ** p < 0.01

32 The Formation of Security Cooperation Networks 30 Table 4: Determinants of Systemic Conflict: Actual and Predicted Network Characteristics Independent Variable Proportion of Wars c Proportion of MIDs c Duration d Baseline Model First Iteration Last Iteration Baseline Model First Iteration Last Iteration Baseline Model First Iteration Last Iteration ABM Predicted Network 0.328** 0.247** 0.855** 0.683** 3.917** 4.424** Polarization (0.075) (0.061) (0.139) (0.11) (1.297) (1.462) Actual Alliance Polarization 0.392* * c 3.626** (0.167) (0.373) (1.346) Capability Concentration (0.288) (0.623) (1.426) Proportion of Major * 0.468* 2.845** 1.401* ** * * Powers (0.09) (0.243) (0.232) (0.955) (0.669) (0.661) (0.56) (1.014) (1.221) Democratic Cliques * * (0.09) (0.212) (1.517) Constant * ** 8.400** 8.389** (0.119) (0.035) (0.033) (0.274) (0.098) (0.095) (0.469) (0.258) (0.276) Rho (AR 1) 0.752** 0.637** 0.423** (0.043) (0.042) (0.045) N F Statistic Adjusted R-Squared D-W Statistic Notes: a Alliance network polarization b Alliance network density c Time-series model with Corchran-Orcutt correction for serial correlation d Autoregressive Poisson model for count data * p <.05; ** p <.01

33 The Formation of Security Cooperation Networks 31 Figure 1: Alliance Networks, 1870, 1974 Alliance Network, 1870 Alliance Network, 1974 Data source: Leeds 2005.

34 The Formation of Security Cooperation Networks 32 Figure 2: Alliance Cliques, 1870, 1974 Alliance Cliques, 1870 Alliance Cliques, 1974

35 The Formation of Security Cooperation Networks 33 Figure 3: Alliance Components, 1874, 1974 Alliance Components, 1870 Alliance Components, 1974

36 The Formation of Security Cooperation Networks 34 Figure 4: Democracy, Strategic Reference Networks (SRNs), and Alliance Networks ABM Results 1. Density 2. Polarization

37 The Formation of Security Cooperation Networks 35 Figure 5: Network Polarization: Actual Alliance Networks and ABM Estimates First Iteration Intermediate Iteration (drawn randomly) Final Iteration year Actual Network Polarization ABM Estimate of NPI Graphs by itertype

38 The Formation of Security Cooperation Networks 36 References Barbieri, Katherine, and Jack S. Levy Sleeping with the Enemy: The Impact of War on Trade. Journal of Peace Research 36 (4): Currrarini, Sergio, Matthew O. Jackson, and Paolo Pin An Economic Model of Friendship: Homophily, Minorities, and Segregation. Econometrica 77 (4): Gibler, D. M. 2008a. The costs of reneging - Reputation and alliance formation. Gibler, Douglas M. 2008b. The costs of reneging - Reputation and alliance formation. Journal of Conflict Resolution 52 (3): Gleditsch, Kristian S Expanded Trade and GDP Data. Journal of Conflict Resolution 46 (5): Hoffmann, Stanley The State of War: Essays in the Theory and Practice of International Relations. New York: Praeger. Jepperson, Ronald L., Alexander Wendt, and Peter J. Katzenstein Norms, Identity, and Culture in National Security. In The Culture of National Security, ed. P. J. Katzenstein. New York: Columbia University Press. Keohane, Robert O., and Joseph S. Nye Power and Interdependence. 2nd edition ed. New York: Random House. Knutsen, Torbjørn L Re-reading Rousseau in the Post-Cold War World. Journal of Peace Research 31 (3): Mansbach, Richard W., and John A. Vasquez In Search of Theory: A New Paradigm for Global Politics. New York: Columbia University Press. Maoz, Zeev Domestic Sources of Global Change. Ann Arbor: University of Michigan Press Realist and Cultural Critiques of the Democratic Peace: A Theoretical and Empirical Reassessment. International Interactions 24 (1): The Street-Gangs of World Politics: The Origins, Management, and Termination of International Alliances. In What Do We Know About War, ed. J. A. Vasquez. New York: Rowman and Littlefield Paradoxical Functions of International Alliances: Security and Other Dilemmas. In Balancing of Power, ed. J. A. Vasquez and C. Elman. Boston: Rowman and Littlefield b. Network Polarization, Network Interdependence, and International Conflict, Journal of Peace Research 43 (4): a. The Effects of Strategic and Economic Interdependence on International Conflict across Levels of Analysis. American Jounral of Political Science 53 (1): Networks of Nations: The Evolution, Structure, and Impact of Interantional Networks, New York: Cambridge University Press Preferential Attachment, Homophily, and the Structure of International Networks, Conflict Management and Peace Science. Maoz, Zeev, and Bruce Russett Normative and Structural Causes of Democratic Peace, American Political Science Review 87 (3): Marshall, Monty G., and Keith Jaggers. Polity IV Project. Center for International Development and Conflict Management, University of Maryland 2004 [cited. Available from Mearsheimer, John J Back to the Future: Instability in Europe after the Cold War. International Security 15 (1): /5. The False Promise of International Institutions. International Security 19 (3): The Tragedy of Great Power Politics. New York: W. W. Norton.

39 The Formation of Security Cooperation Networks 37 Oneal, John, and Bruce Russett Rule of Three, Let it Be: When More Really Is Better. Conflict Management and Peace Science 22 (4): Pevehouse, Jon, Timothy Nordstrom, and Kevin Wranke The Correlates of War 2: International Governmental Organizations Data, Version 2. Conflict Management and Peace Science 21 (2): Powell, R Absolute and Relative Gains in International Relations Theory. American Political Science Review 85 (4): Riker, William The Theory of Political Coalitions. New Haven, CT: Yale University Press. Siverson, R. M., and J. Emmons Birds of a Feather: Democratic Political Systems and Alliance Choices in the 20th Century. Journal of Conflict Resolution 35 (2): Snidal, D. 1991a. International Cooperation among Relative Gains Maximizers. International Studies Quarterly 35 (4): b. Relative Gains and the Pattern of International Cooperation. American Political Science Review 85 (3): Waltz, Kenneth N Theory of International Politics. New York: Random House. Wasserman, Stanley, and Katherine Faust Social Network Analysis: Methods and Applications 2nd ed. New York: Cambridge University Press. Watts, Duncant J., and Steven H. Strogatz Collective dynamics of 'small-world' networks. Nature 393 (6684):440-2.

40 The Formation of Security Cooperation Networks 38 Appendix: Detailed Structure of ABM Figure 3 displays the flow chart of the ABM model in its simplest form. Figure 3 about here First Iteration: 1. The simulation assigns random values to five square matrices of order n (number of states). (a) The SRN 0 matrix defines the strategic reference network at time t 0. Entries in this matrix srg ij are 1 if state j is a member of state s i SRG, and zero otherwise. This matrix is updated as the simulation unfolds. (b) The capabilities (C) matrix is a diagonal matrix with entries 0 < c ii < 1 and all other entries are zero ( c ii =1). Entries reflect the system s share of military capabilities owned by each of the states. (c) the MID matrix with values mid ij =1 if states i and j had a MID and zero otherwise. (d) The DEM matrix defines the network of joint democracies (dem ij =1 if states i and j are both democracies). (e) The joint cooperation matrix JC with entries jc ij assuming the value of one if both states had a history of joint cooperation, and zero otherwise. All matrices except the SRN are fixed over the set of iterations of a given run. 2. The focal state calculates its Alliance Opportunity Cost (AOC i0 ) by subtracting its own capabilities from the aggregated capabilities of its SRG members. For state i this is defined as n AOC srgc c (where SRGC 0 = SRG 0 C, and c i are state i's capabilities). i0 ij0 i j 1 3. If a state s AOC i0 is smaller than or equal to zero then the state does not require allies; it can meet external challenges through the application of its own capabilities. 4. If AOC i0 > 0 the gap between the state s capabilities and the cumulative capabilities of its PRIE defines the extent to which the state needs allies. 5. This starts the ally search module: The first step in the module applies only to democracies. First, we calculate the democracy capability matrix. This is accomplished by DC = (D SRG) C. If the focal state is not a democracy the row corresponding to the state s index number will be zero.

41 The Formation of Security Cooperation Networks 39 If it is a democracy, it will have at least one non-zero entry in its corresponding row. Because states apply the size principle, the focal state i goes to the largest dc ij entry in its row. Second, an Expected Alliance Capabilities (EAC) matrix is established, and the state enters eac ij = dc ij for the jth entry in DC i (the ith row of matrix DC), with j being considered as a would-be ally. Thus, the EAC matrix reflects the capabilities of i's would-be allies. Next, the focal state updates its AOC. The new AOC is defined as AOCi 0 srgcij 0 ( ci eacij ) n where eac ij is the capability a j 1 would-be ally of i. 6. If the revised AOC is still larger than zero, the state adds the capabilities of the second largest entry in the respective row of DC to EAC, and updates the AOC. 7. This process continues until, (a) AOC i0 0, or (b) all entries in the respective row of the DC matrix were added into the EAC of state i. This means that the focal (democratic) state has already approached all of the other democracies that are not part of its SRG and has added their capabilities to its own, yet it requires additional allies to balance against its SRG. 8. This starts the enemy of my enemy module, which applies to all states whether or not they are democratic. The focal state screens its environment for states with which it share enemies. The Enemy of my Enemy (EE) matrix is obtained by a binarized squared MID matrix (see Maoz et al., 2007). EE = B(MID 2 )-SRG. The capabilities of states with common enemies are obtained in EEC = EE C. 9. Just as in the previous case, the focal state i selects the largest entry in EEC i and updates its EAC and its AOC as in step 5 above. This process continues until (a) AOC i0 0, or (b) all entries in EEC i have been exhausted. 10. If AOC i0 > 0 after step 9, we move to the joint cooperation module. Here too, we calculate a Joint Cooperation Capabilities matrix JCC = (JC SRG) C. The focal state goes to the largest j i

42 The Formation of Security Cooperation Networks 40 entry in JCC i, adds its capabilities and updates its EAC and AOC i0 as in step 5 above. This process continues until a) AOC i0 0, or (b) all entries in JCC i have been exhausted. 11. Once this is completed, an expected alliance matrix (EA 1 ) is defined with the following values: ea 1ij 1 if eaij ea ji 1 0 otherwise Thus, the expected alliance matrix reflects only actual alliances. An actual alliance is one where both members consider each other as a potential ally. Subsequent Iterations: 1. Each state revises its SRG matrix such that SRG1 B( SRG0 MID EA1 ). Where B is a binarization operation of the sum. This updated SRG matrix now reflects a strategic reference network in which the alliances that were formed in the previous iteration become part of the determination of each state of the security challenges it faces. This is an important step because states consider the allies of their enemies as potential challengers of their security. 2. Once this update occurs, the iteration follows the same loops as the first iteration. Each iteration, then, ends with an EA t matrix where t indexes the iteration (time). Termination Conditions. 1. At the end of each iteration the model compares the current EA t matrix to the previous matrix EA t-1. If EA t EA t-1 = 0, the run ends. This indicates that none of the alliances has changed due to the update of individual SRGs, and thus implies an equilibrium convergence. 2. Alternatively, a maximum number of allowable iterations is specified by the user. If the current iteration t equals that maximum, the run ends. ABM Output The process outputs all the input matrices, and in addition the updated SRG t and EA t matrices for each iteration t = 0, 1, k.

43 The Formation of Security Cooperation Networks 41 Figure A1: Structure of the Realist Version of the Agent-Based Model of Alliance Network Formation