Information Mechanisms

A long-standing assumption in international relations is that, due to systemic anarchy, states lack credible information about one another's preferences (Keohane Reference Keohane1984; Waltz Reference Waltz1979). Consequently, states cannot determine whether potential partners wish to cooperate for mutual gain or instead wish to secure gains through defection (Kydd Reference Kydd2005). States may also harbor more benign concerns about whether partners possess sufficient resources to maintain treaty commitments (Chayes and Chayes Reference Chayes and Chayes1996). Questions about trustworthiness and reliability are the driving force behind collaboration problems. States require information about both the willingness and the ability of potential partners to meet institutional obligations. Third-party ties provide this information by identifying targets that one's own partners have deemed trustworthy and capable.

In interpersonal networks, third-party ties encourage trust—and, thus, triadic closure—through i and j’s mutual affect toward k. In interstate networks, in contrast, trust emerges via the risks of cooperation. Kydd (Reference Kydd2005) shows that when states lack information about one another's preferences, incremental acts of cooperation function as costly signals. Sufficiently risky cooperative overtures reveal a state to be a cooperative type rather than an exploitative type, willing to accept some risk of defection for the sake of mutual benefit. Signaling arguments are usually dyadic, such that signals only matter to those actors directly involved in bargaining, but signals also have implications for external observers. Consider again Figure 2(d). For any i partner of k, the kj ₄ tie indicates, first, that k has deemed j ₄ sufficiently trustworthy to risk reciprocal cooperation, and, second, that in k’s determination, j ₄ is capable of meeting its institutional obligations. Further, through its own relationship with k, state i has first-hand knowledge of k’s evaluative standards and risk propensity—information that, in null or partial triads, i would not likely possess. The kj ₄ tie thus conveys nontrivial information about j ₄ to k’s existing partners. In general, network ties provide a credible third-party assessment of a prospective partner's reliability and trustworthiness.

Concerns about trust and reliability plague numerous issue areas but are perhaps most apparent in military cooperation. Consider, for example, relations between Japan and South Korea, long characterized by mistrust. The United States, an integral k third party, has deliberately targeted trust dilemmas as a means of promoting greater Japan-Korea cooperation (Cha Reference Cha1999), such that “a failure of US commitment only increases insecurity and mutual mistrust” (Green Reference Green1999, 23). In this triadic context, Japan and Korea's respective ties to the US provide information about one another's cooperative intent and potential contributions to bilateral actions. In the mid-2000s, the US signed separate bilateral military agreements with both Japan and Korea, including agreements on general sharing of military intelligence (GSOMIA) and on mutual logistical support (MLSA). Shortly thereafter, supporters of bilateral cooperation began pushing for similar agreements between Korea and Japan. A prominent Korean academic referred to the absent Korea-Japan agreements as a “missing link,”Footnote ⁸ and Korean newspapers argued that closing the triad would allow more efficient use of Japanese satellite technology and logistical support.Footnote ⁹ In early 2011, in a historically unprecedented move, defense ministers from Japan and Korea met to discuss implementation of both a GSOMIA and MLSA,Footnote ¹⁰ thus initiating a dialogue that, arguably, would not have materialized without the pressures and incentives created by each state's respective ties to the US.

In addition to trust dilemmas, states may fail to cooperate if they disagree over distributions of gains. With complete information, such coordination problems are entirely distributional, but states often lack information about the precise distributional impact of different institutional arrangements and are thus unsure of one another's preferred outcomes. If states share private information and pool their technical knowledge, they may discover that they both prefer the same institutional design—in which case cooperation follows unproblematically. Yet, states have incentives to withhold private information. For example, a state may know that a particular set of institutional rules will disproportionately benefit itself, and revealing this information would lower the probability of that outcome being chosen by others (Morrow Reference Morrow1994). Incentives to withhold information can thus prevent cooperation even when mutually acceptable agreements exist.

Morrow (Reference Morrow1994) argues that international regimes diminish coordination problems by structuring communication and facilitating exchange of information (cf. Keohane Reference Keohane1984). Network ties function analogously. Specifically, a state's third-party ties indicate the types of agreements that are acceptable to that state. Thus, bilateral agreements between i and k partially reveal i’s preferences on design issues such as scope of agreement, monitoring and enforcement mechanisms, escape clauses, flexibility and renegotiation, and so on (cf. Koremenos, Lipson, and Snidal Reference Koremenos, Lipson and Snidal2001). Importantly, agreements between j and k reveal precisely the same information about j; the mutual {ik, jk} ties of an unclosed triad thus maximize information provision. Further, because i and j have both forged bilateral agreements with a common k third party, there likely exists a correspondence of interests between them, reflected by their mutual interest in cooperation with the same partner; consequently, their preferences are more likely to overlap, such that, when those preferences are revealed, rather than competing over divergent outcomes, both actors readily converge on a single mutually preferred outcome. Again, these mechanisms only obtain in the unclosed triad in Figure 2(d) and, all else constant, should be weak or nonexistent in null or partial triads.

Empirical evidence shows that third-party ties do indeed act as informal precedents. For example, early US trade agreements with Singapore and Chile served as “bellwether” treaties that “set the substantive parameters” and generated “precedent-setting effect[s]” for future agreements (Weintraub Reference Weintraub and Schott2004). The US-Singapore agreement—the first such agreement between the US and an Asian country—informed other Asian states of US standards on contentious issues like trade in services, government procurement, intellectual property, investment protection, labor standards, and environmental regulation (Weintraub Reference Weintraub and Schott2004, 89). The US-Chile agreement accomplished similar goals with respect to Latin American countries (Feinberg Reference Feinberg2003; Weintraub Reference Weintraub and Schott2004). The agreements appear to have been relatively successful in this regard, as they opened doors to trade talks between the US and additional partners in both regions (Feinberg Reference Feinberg2003). Thus far, the US has “closed the triad” with three of Chile's FTA partners—Colombia, Peru, and Panama.

Many bilateral agreements involve coordination and collaboration simultaneously (Fearon Reference Fearon1998). Consider the postwar emergence of cultural and scientific exchange between the US and the Soviet Union. Both states viewed such exchanges as inherently strategic endeavors (Bu Reference Bu1999; Gould-Davies Reference Gould-Davies2003). The US feared that Soviet visitors would engage in espionage and propagandizing, while the Soviets worried about the influence of American media. In 1955, at the four-power summit in Geneva, the adversaries discussed a variety of exchange agreements, but their strategy of rejecting concessions and pursuing “unilateral advantage” doomed the proceedings (Hixson Reference Hixson1997, 106). Not only did the US and USSR doubt one another's trustworthiness, but they also disagreed on how to structure the agreement itself, especially regarding the size, scope, and duration of exchanges. A Soviet cultural minister later discussed his country's bargaining position: “[f]or us, the most favorable forms of agreements on cultural cooperation with capitalist states are cultural agreements . . .[that] contain only general principles of cooperation (mutual understanding, friendship . . .cultural relations . . .) and do not fix any concrete measures on the two sides.”Footnote ¹¹ The US, on the other hand, favored explicit assurances of “equality, reciprocity, and mutual benefit” (Richmond Reference Richmond2003, 17). The historic Zarubin-Lacy agreement was eventually signed in 1958, but not before the USSR had established bilateral exchange agreements with key US allies: Belgium and Norway in 1956, and France and the UK in 1957 (Richmond Reference Richmond2003). These agreements were landmarks for the USSR and the new Khruschev regime. Not only did they reveal Soviet obduracy on particular questions of institutional design, but they also signaled that, in the minds of US allies, Khruschev was acceptably trustworthy on matters of cultural exchange. Subsequently, consistent with the logic of triadic closure, Zarubin-Lacy prompted agreements between the US and other Eastern-bloc states, including Romania, Poland, and Yugoslavia (cf. Bu Reference Bu1999).

Externalities Mechanisms

Cooperation may provide access to otherwise unattainable gains, but these gains vary in size, and the “gap in gains” between exploitative and cooperative outcomes also conditions the probability of cooperation (Lipson Reference Lipson1984). If prospective gains are small, states will be less motivated to cooperate. Similarly, the lower a state's costs for noncooperation, the more likely it is to bargain hard, thus lowering the probability of successful coordination (Fearon Reference Fearon1998). Third-party ties influence cooperation by enlarging this gap in gains. Reconsider Figure 2. Holding all else constant (including trustworthiness), a given i should be more likely to cooperate with j ₄ than with j _1,2,3 precisely because, relative to the noncooperative outcome, the ij ₄ tie yields the highest payoff. This is so because unclosed triads generate negative externalities while simultaneously promising beneficial externalities.

First, unclosed triads generate negative externalities that materially deteriorate i and j’s status quo relationship, pressuring them to cooperate with one another directly due to an increasing gap in gains. The precise form of these externalities is issue specific, but they are widely apparent across issue areas. For example, preferential trade agreements (PTAs) create negative externalities insofar as reduced tariffs encourage trade diversion from more efficient nonmember producers to less efficient PTA members (Bagwell and Staiger Reference Bagwell and Staiger1997). When an unclosed PTA triad forms, importers in both i and j switch to k, who benefits disproportionately. Forming a PTA thus allows i and j to restore the more efficiently produced imports they previously received from one another (Manger, Pickup, and Snijders Reference Manger, Pickup and Snijders2012).Footnote ¹² Similarly, unclosed security triads prevent efficient cooperation on military issues. For example, GSOMIAs explicitly restrict sharing of classified information with third parties; in an unclosed triad, i may have limited access to security information from k if that information was previously shared with or received from j.

These pressures are apparent even in areas such as environmental regulation. Consider the bilateral fisheries agreements negotiated among China, South Korea, and Japan following entry-into-force of the UN Law of the Sea Convention in 1994. The Japan-Korea agreement was implemented first, in January 1999, replacing a bilateral pact that had endured since 1965. Next came the China-Japan agreement, which entered into force in June 2000 and replaced a series of agreements dating to 1955. Korea-China cooperation proved less tractable. These two states lacked formal diplomatic relations until 1992, had no prior agreements to draw upon, and largely engaged in “free fishing activities” (Kim Reference Kim2003, 104). Yet, the Japan-Korea agreement delineated Korean fishing rights in areas also accessible to China, creating the potential for jurisdictional disputes (Kim Reference Kim2003). At the same time, the China-Japan agreement severely limited China's access to Japanese waters; China requested access for 4,000 vessels, but Japan allowed only 600.Footnote ¹³ These restrictions pushed Chinese fishermen into Korean waters, where they targeted the same fish as their Korean counterparts (Kang Reference Kang2003) and, indeed, quickly exceeded the catch of Korean ships.Footnote ¹⁴ As a direct consequence of these externalities, Korean officials demanded an acceleration of talks on fisheries regulation.Footnote ¹⁵ China, eager to clarify jurisdictional obligations, readily accommodated. A Korea-China agreement ultimately entered into force on June 30, 2001, closing the triad.

Second, bilateral agreements generate positive externalities by establishing reference groups of like-minded cooperators. States often use institutional affiliations to define specific ingroups and outgroups, as evidenced by such informal clusterings as the Soviet bloc, the nonaligned states, the developed world, the global south, and others (Hafner-Burton and Montgomery Reference Hafner-Burton and Montgomery2006). These reference groups consist of states that hold relatively similar preferences and tend to interact more with one another than with outsiders. Triadic closure is a small-scale form of group cohesion; when actors prefer ties to “friends of friends” over ties to unaffiliated others, they effectively favor ingroup over outgroup relations. Studies of group dynamics typically explain ingroup favoritism in terms of social-psychological mechanisms, but in international relations, favoritism is likely strategic. Group membership promises such beneficial externalities as deepened economic relations, security umbrellas, and multilateral organizations. By focusing their ties on the reference group, states increase the potential gains of cooperation beyond the immediate payoffs of bilateral agreements.

Cases of regional integration offer especially compelling examples. Consider the relationship between the Andean Community (CAN) and Mercosur. In 2004, in response to accumulating bilateral economic and other ties between members of the two organizations, Mercosur extended associate membership to all members of CAN. In 2005, CAN reciprocated. Bilateral ties thus initiated a series of long-term club goods: expanded institutional memberships, deepened economic integration, and the eventual development of a larger South American Union (UNASUR), which extends to such contentious issue areas as immigration, education, energy security, and even defense policy. Tellingly, Chile is a full member of neither Mercosur nor CAN (having left the latter in 1976) but, due to its extensive bilateral ties to other South American countries, is a founding member of UNASUR. Of course, Latin American states also share agreements with extra-regional actors. Triadic closure simply means that, ceteris paribus, the baseline probability of cooperation is generally highest among the ingroup, where long-term club goods are most likely to accrue.

Hypotheses and Additional Network Influences

Information and externality mechanisms are complementary. As the number of k third parties with whom i and j share agreements grows, information mechanisms reduce the risk of bilateral cooperation while externality mechanisms increase the relative benefits, generating third-party incentives for direct ij cooperation. Importantly, the generality of these mechanisms means they are broadly applicable to a wide variety of issue areas—an implication I empirically verify later in the article. The discussion of triadic closure thus yields the following hypothesis:

Though I focus primarily on triadic closure, other network influences may be apparent. In particular, states may prefer to cooperate with partners that simply form more bilateral agreements in general, irrespective of whether they share partners in common. Figure 3(a) illustrates preferential attachment, where i’s probability of creating a tie to any given j target depends on that target's “degree centrality,” or overall number of network ties (Barabási and Albert Reference Barabási and Albert1999). In terms of the proposed causal mechanisms, high-degree targets may convey trustworthiness and reliability more credibly than their low-degree counterparts. During the 1990s, for example, Japan increased security cooperation not only with the US but also with major European powers, which, to a third party like South Korea, may suggest a general interest in cooperation. As well, the more agreements a state enters, the more information it reveals about its preferences over institutional designs. When the USSR began signing exchange treaties in the 1950s, outside observers of all varieties, even those who lacked an explicit “friend of a friend” connection, gained insight into the types of agreements the Soviets found acceptable. In terms of externalities, partnerships with high-degree states promise greater rewards, as creating a tie to a high-degree j engenders indirect ties to—and thus improves prospects for direct cooperation with—j’s numerous k partners. For all these reasons, high-degree states should endogenously attract further cooperative ties.

FIGURE 3. Additional Network Influences

Note: Solid lines indicate bilateral cooperation agreements. Dashed lines indicate prospective agreements. Gray arrows indicate ties or similarities in exogenous covariates.

Closure and attachment are perhaps the most fundamental processes in complex networks (Newman Reference Newman2003b). I nonetheless expect the former to have a stronger substantive impact on cooperation than the latter. In anarchy, cooperation hinges crucially on credible information. Because triadic ties involve trusted intermediaries—specifically, i and j’s mutual k partners—they should generally be a more credible source of information than the myriad ties of high-degree states. During the Cold War, for example, the US and the USSR were both high-degree actors, but perceptions of their relative trustworthiness differed sharply. As well, the externalities generated by unclosed triads—particularly the negative externalities—should have a more immediate and salient impact than the more diffuse externalities generated by ties to high-degree states. And if i’s tie to a particular j hub leads, ipso facto, to unclosed {ij, jk} triads, then a triadic closure process, rather than an attachment process, will govern the subsequent formation of ik ties. Thus, while I expect both effects to be significant, the effect of closure should be substantively stronger.

Finally, cooperation between i and j may also depend on similarities and connections between the prospective partner, j, and i’s existing k partners. Consider Figure 3(b). The solid line denotes a bilateral cooperation agreement, while the gray j ↔ k arrow indicates either that k and j share a tie on some other dimension—e.g., a military alliance or geographic border—or that they share a common attribute, such as regime type. Covariate closure effects involve interactions between network ties and exogenous covariates and, in network terms, represent an indirect form of homophily—commonly known by the idiom “birds of a feather flock together” (McPherson, Smith-Lovin, and Cook Reference McPherson, Smith-Lovin and Cook2001; Newman Reference Newman2003a). Homophily is typically conceptualized dyadically, where similarities between i and j increase their probability of direct cooperation (e.g., Maoz Reference Maoz2012). I extend the homophilic principle to third parties, such that similarities and connections between i’s current and potential partners condition i’s network activity.

Covariate closure effects provide an important control relative to the main network effects, particularly triadic closure. Contrary to Hypothesis 1, i may simply favor j partners who are connected to and/or share similarities with its existing k partners, irrespective of whether those j states share bilateral agreements with k. Thus, if the US-Chile trade agreement sets a precedent for Latin American countries, then the US-Chile tie should increase cooperation between the US and Chile's geographic neighbors. Although such a dynamic is distinct from triadic closure, it may be motivated by similar mechanisms. For example, i may view states who share important traits with its current partners as being equally trustworthy and/or equally capable of meeting their institutional obligations, or i may pursue ties to homogeneous clusters of states in order to establish stable reference groups of collaborators. The empirical analysis considers a variety of possible jk connections. In general, covariate closure yields the following expectation:

A possible counterargument to Hypothesis 1 is that because cooperation is risky, states may prefer to reap benefits from indirect ties rather than engaging in triadic closure (cf. Bala and Goyal Reference Bala and Goyal2000). Closure effects should prevail for at least three reasons. First, unlike multilateral agreements, bilateral agreements can be undone by just one state, which increases the risks of free riding; the prospect of negative externalities further increases that risk. Second, gains accrued via indirect ties are qualitatively different than the gains of a direct tie. A given i may benefit from, say, a trade deal between j and k, but any such benefits will differ starkly from the preferential market access of a direct agreement. Third, many agreements—such as those focused on security issues or scientific research—explicitly prohibit signatories from sharing the gains of cooperation with third parties. Overall, then, direct bilateral cooperation, backed by credible information on the preferences of one's partners, remains the most reliable source of gains.

Another potential counterargument is that the proposed network effects—preferential attachment and triadic closure—are contradictory rather than complementary. This possibility originates in the vast literature on network emergent properties, where the respective attachment and closure processes lead to divergent network topologies: in the former case, a “scale-free” network with numerous low-degree nodes and a few very high-degree nodes (Barabási and Albert Reference Barabási and Albert1999), and in the latter case, a highly clustered network (Watts Reference Watts1999; Watts and Strogatz Reference Watts and Strogatz1998). In practice, real-world networks are commonly both scale-free and highly clustered (Newman Reference Newman2003b; Ravasz and Barabási Reference Ravasz and Barabási2003). Indeed, attachment and closure lead to divergent topologies only when the dynamical rules of network growth incorporate one process to the exclusion of the other—as may be the case, for example, in synthetic networks, where network processes reflect fundamental nodal preferences (Klemm and Eguiluz Reference Klemm and Eguiluz2002). In the present analysis, attachment and closure are not preferences but strategies that states use to achieve a much more fundamental interest: maximizing the gains of cooperation while minimizing risks. As strategies directed toward a common goal, the two processes are complementary. The SI nonetheless thoroughly explores the topology of the cooperation network and shows that it is both scale free and nontrivially clustered.

Data on Bilateral Cooperation Agreements

Cooperation agreements cover a wide array of issues. To ensure applicability of the analysis to the breadth of international cooperation, I employ Rohn's (Reference Rohn1984) topic codes to locate issue-specific clusters of agreements within broader economic, security, cultural, and environmental categories. Focusing on issues that are both politically salient and strategically relevant, I code agreements in four areas. First, agreements on trade in commodities (Commodity) involve import and export of raw materials, such as metals and agricultural products.Footnote ¹⁶ Second, nonalliance military agreements (Military) involve such issues as transfer of classified information, exchange of personnel, stationing of equipment, and collaboration in defense industries.Footnote ¹⁷ Third, agreements in the sciences (Sciences) promote research and cultural exchange in science and technology.Footnote ¹⁸ Finally, fisheries agreements (Fisheries) involve demarcation of fishing zones, catch quotas, industry regulation, and inspections.Footnote ¹⁹ Taken as a whole, these agreements cover cooperation problems across the major fields of international relations. Further, the categories are sufficiently narrow as to generate issue-specific externalities—whether negative or positive—for relevant third parties.

The key impediment to coding bilateral agreements is that, because such agreements are not as closely monitored as their multilateral counterparts, data collection depends largely on country reports. Many countries publish annual lists of agreements, but others wait years or even decades between publications. Network models are highly sensitive to missing data (Kossinets Reference Kossinets2006). To minimize missingness, I restrict the sample to the period from World War II to 1980, for which data on bilateral agreements are most reliable and complete.Footnote ²⁰ This temporal span maximizes data coverage while also focusing the analysis on precisely the period in which bilateral agreements first proliferated. The data are drawn from the World Treaty Index (WTI)—initially published by Rohn (Reference Rohn1984) and later updated by Bommarito, Katz, and Poast (Reference Bommarito, Katz and Poast2012)—and cover all independent states in the international system.Footnote ²¹ In total, the sample includes 1,709 agreements: 413 in Commodity; 475 in Military; 486 in Sciences; and 335 in Fisheries.

The data must be coded such that empirical analysis can determine the effect of existing bilateral agreements on the creation of new agreements. While bilateral agreements often endure for many years, historical evidence suggests that network effects are strongest within the first few years of a tie's creation. Network pressures led to a Korea-China fisheries agreement in less than a year. Cultural cooperation between the US and USSR emerged within two years of the USSR's other agreements. Even in the case of long-term externalities, such as those generated by regional integration, states respond to the immediate promise of future gains; they need not wait for these gains to materialize. I therefore employ a flexible coding of agreements, y_ij, such that

(1)\begin{equation} y_{ij}= \left\lbrace \begin{array}{ll} 1 &\quad \mbox{if an agreement between $i$ and $j$ entered} \\ &\qquad \mbox{into force within the past $\tau $ years,} \\ 0 &\quad \mbox{otherwise}, \end{array} \right. \end{equation}

Modeling Network Influences

IR scholars have grown increasingly attuned to the methodological challenges posed by interdependencies in relational data.Footnote ²⁴ The logit and probit models commonly used to analyze binary dyadic data assume that observations of the dependent variable are identically and independently distributed.Footnote ²⁵ When dependencies exist, traditional estimation methods are misspecified and may produce biased estimates.Footnote ²⁶ In response, IR scholars have begun exploring new models for dyadic data, including spatial regression techniques (Franzese and Hays Reference Franzese and Hays2007; Neumayer and Plümper Reference Neumayer and Plümper2010), latent space models (Hoff and Ward Reference Hoff and Ward2004), and strategic interaction specifications (Signorino Reference Signorino1999). By accounting for various dependencies, these approaches improve estimation of exogenous covariates. Because the theory treats dependencies themselves as substantively interesting, the analysis requires a model that allows for estimation of such precise endogenous effects as triadic closure, preferential attachment, and covariate closure. Exponential random graph models (ERGMs)—the workhorse of statistical inference in network analysis (Robins et al. Reference Robins, Pattison, Kalish and Lusher2007)—allow estimation of such effects but are generally limited to cross-sectional analysis.Footnote ²⁷

Ultimately, methodological choices should be motivated by theory. I argue that bilateral agreements constitute a global network, where the structure of that network drives the creation of new agreements. To model this data generating process, I employ a stochastic actor-oriented model (SAOM) of network evolution, which treats the network itself as the dependent variable and models the influences, both endogenous and exogenous, that lead to changes in the network over time.Footnote ²⁸ Those changes are assumed to result from the purposive, utility-maximizing decisions of individual actors, who evaluate their positions in the network and adjust their ties so as to maximize their utility (Snijders Reference Snijders2001, Reference Snijders, Carrington, Scott and Wasserman2005). The SAOM thus presumes individual initiative, which is consistent both with the theory and with strategic-choice approaches to international relations more generally (e.g., Lake and Powell Reference Lake and Powell1999). Because estimation relies upon repeated simulations of a specified model of network evolution, as described below, the approach is methodologically equivalent to employing an agent-based model for purposes of statistical inference (Snijders, van de Bunt, and Steglich Reference Snijders, van de Bunt and Steglich2010, 46). Here, I briefly describe the model.Footnote ²⁹ The SI contains an in-depth discussion.

Let Y be an n×n matrix, where the y_ij elements of Y are defined according to Eq. (1), and i, j = 1, . . . , n. For a given year of data, Y represents the entire bilateral cooperation network, and each y_ij entry indicates a specific network tie. Since the network is dichotomous, these ties take on values of either zero or one. As well, since cooperation agreements are nondirected, y_ij = y_ji. Observing the network at m points in time (e.g., years) yields a time series of network observations, Y(t_m). The model assumes that these observations are discrete moments in an unobserved continuous process of network evolution, where the evolution of the network follows a Markov process, such that the structure of the network at t_m determines the structure of the network at t _{m + 1}, subject to stochastic error and exogenous covariates (Snijders Reference Snijders, Carrington, Scott and Wasserman2005, 227).Footnote ³⁰ Between moments, the network evolves one tie at a time, as a consequence of individual actors extending and retracting ties. The accumulation of these ties, measured at each observation moment, determines the extent of change or evolution in the network. Explaining change in network structure is thus a matter of identifying those factors that influence actors’ individual choices. The model assumes that, when selecting partners, i maximizes a so-called objective function, f_i(β, y), represented as a linear combination of endogenous network influences and exogenous covariates (Snijders Reference Snijders2001, Reference Snijders, Carrington, Scott and Wasserman2005). Formally,

(2)\begin{equation} f_i(\beta ,\mathbf {y})= \sum ^{L}_{h=1}\beta _h s_{ih}(\mathbf {y}), \end{equation}

Because bilateral agreements require mutual consent, the creation of a new tie depends on the objective function as applied to both i and j. Specifically, i proposes a tie to whichever j maximizes f_i(β, y), and the tie is created only if it also increases j’s utility.Footnote ³¹ In principle, actors may maximize the objective function through both creation and termination of ties. However, because the theory emphasizes creation of new agreements and is agnostic about termination, and because tie duration is defined exogenously (see Eq. (1)), the analysis focuses only on the creation of new ties.Footnote ³² Once i and j create a tie, the tie endures as defined by Eq. (1), and the structure of the network changes correspondingly—which in turn determines the probability distribution for creation of subsequent ties for all actors. In the SI, I vary these restrictions.

The model is too complex for direct calculation of probabilities. I instead obtain estimates using method of moments, which determines parameters by minimizing the difference between the observed and expected values of the s_ih(y) functions. Observed values are given by the data, while expected values—which are unknown ex ante—must be drawn from repeated Markov chain Monte Carlo simulations of the network using randomly sampled values of the β parameters (Snijders Reference Snijders2001). Parameter estimates are given by the vector $\skew4\hat{\beta }$ that minimizes the absolute difference between the calculated values of the s_ih(y) statistics in the observed and simulated networks. Convergence is checked by assessing deviations in the simulated network statistics from their targeted or observed values (Ripley, Snijders, and Preciado Reference Ripley, Snijders and Preciado2012). The SI describes this simulation procedure in detail.

By modeling network evolution in continuous time, the SAOM allows inferences to be drawn even from network ties that appear to emerge simultaneously—such as a triad that is null at t ₁ but fully closed at t ₂. Further, the model treats network ties not as singular events but as indicative of a relatively stable “condition” or “state” with enduring structural effects (Snijders, van de Bunt, and Steglich Reference Snijders, van de Bunt and Steglich2010, 45), which allows us to determine how a given “state” of the network conditions the creation of new network ties—and how tie creation in turn affects the structure of the network. At the same time, because the model shares key characteristics with logistic regression, hypothesis testing is conducted similarly to traditional models, by calculating t-statistics from estimated coefficients and standard errors.

Network Effects and Covariates

Network influences are modeled as s_ih(y) components of the objective function, as defined in Eq. (2).Footnote ³³ The first effect, TriadClosure, which tests Hypothesis 1, is defined for a given i as

(3)\begin{equation} s_{i1}(\mathbf{y}) = \displaystyle \sum_{j\lt k}^{n} y_{ij} y_{ik} y_{jk},\quad i \ne j \ne k. \end{equation}

A positive β₁ estimate indicates that, in evaluating the network and proposing new agreements, states favor ties that lead to closed triads. Figure 4 maps third-party ties or “2-paths” at two observation moments. For purposes of illustration, the figure shows both fully closed {ik, kj, ij} triads and potentially closable {ik, kj} triads (i.e., where only the direct ij tie is missing). More proximate nodes share more third-party ties with one another than with other nodes (and thus share more “friends of friends” in common), while larger nodes have more third-party ties in general. Bilateral cooperation should be most likely between large, proximate nodes. The graphs reveal an interesting trend. In 1960, bilateral agreements largely reflected Cold War factions, with Western and NATO-bloc states clustered in the upper-left of the graph, and Eastern bloc states clustered on the opposite side. By 1980, the landscape shifted substantially, with the US sharing extensive indirect ties to such ideological adversaries as East Germany (GDR), Poland (POL), and the Soviet Union (RUS). Such a shift should, in turn, improve the odds of direct East-West cooperation.

FIGURE 4. Third-Party Ties in Bilateral Cooperation Agreements, 1960 and 1980

Note: Based on Agreement coding, τ = 3. Proximity of nodes indicates number of shared 2-paths. Node size indicates each node's total number of 2-paths. Node positions determined by multidimensional scaling with slight jittering to increase readability. Only states with a nodal degree of 2 or greater are shown.

The PrefAttachment effect, defined in terms of j’s degree centrality, is

(4)\begin{equation} s_{i2}(\textbf {y}) = \displaystyle \sum _{j}^{n}y_{ij}\sum _{k}^{n}y_{jk}, \end{equation}

FIGURE 5. Degree Centrality in Bilateral Cooperation Agreements, 1980

Note: Based on Agreement coding, τ = 3. Darker shading indicates greater degree centrality.

Finally, to test Hypothesis 3, let z_jk = z_kj represent a bilateral connection or shared characteristic between some prospective partner, j, and some third party, k. Then, the statistic

(5)\begin{equation} s_{i3}(\textbf {y}) = \displaystyle \sum_{j\ne k}^{n}y_{ij}y_{ik}z_{jk} \end{equation}

The model incorporates a standard battery of controls as additional s_ih(y) components of the objective function. At the dyadic level, I include distance (Gleditsch and Ward Reference Gleditsch and Ward2001), contiguity (Correlates of War Project 2006), shared IGO membership (Pevehouse, Nordstrom, and Warnke Reference Pevehouse, Nordstrom and Warnke2004), trade dependence (Barbieri and Keshk Reference Barbieri and Keshk2012), and military alliances (Leeds et al. Reference Leeds, Ritter, Mitchell and Long2002). I also include three monadic covariates—democracy (Marshall and Jaggers Reference Marshall and Jaggers2002), military capabilities (Singer Reference Singer1987), and per-capita GDP (Gleditsch Reference Gleditsch2002)—and their ij interactions.Footnote ³⁴